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ON  SENSATIONS  FROM  PRESSURE  AND  IMPACT 

Frederic  S.  I 

Columbia  CoU 
New  York 

WITH   SPECIAL   REFERENCE  TO    THE    INTENSITY 
AREA   AND   TIME    OF    STIMULATION 


BY 

IIAKOLI)  GRIFFING,  A.B. 


SUBMITTED    IN    PARTIAL    FULFILMENT    OV    THE    REQUIREMENTS 

FOR    THE    DEGREE    OF    DOCTOR    <>F    PHILOSOPHY 

IN   THE 

University  Faculty  of   Philosophy 
Columbia  College 


NEW   YORK 
1895 


ON  SENSATIONS  FROM  PRESSURE  AND  IMPACT 


WITH   SPECIAL  REFERENCE  TO    THE   INTENSITY 
AREA  AND   TIME   OF   STIMULATION 


BY 

HAROLD  GRIFFIKG,  A,B. 


SUBMITTED    IN    PARTIAL    FULFILMENT    OF    THE    REQUIREMENTS 

FOR    THE    DEGREE    OF    DOCTOR    OF    PHILOSOPHY 

IN   THE 

University  Faculty  of   Philosophy 
Columbia  College 


NEW  YORK 
1895 


CONTENTS, 


Introduction, 


PAGE 

I 


Sec. 
Sec. 
Sec. 
Sec. 
Sec. 


CHAPTER  I. 

The  Quality  of  the  Stimulus. 

Semi-organic  Sensations  and  their  Stimuli     .    .    . 

Sensations  of  Touch  and  Temperature 

Active  Touch . 

Passive  Touch 

The  Classification  of  Dermal  Sensations 


Sec.  I 

Sec.  2 

Sec.  3 

Sec.  4 

Sec.  5 

Sec.  6 

Sec.  7 


CHAPTER  II. 

The  Intensity  of  the  Stimulus. 

The  Concept  Intensity lo 

Touch  and  Pressure        ii 

The  Threshold  for  Pain 14 

The  Range  of  Pressure  Sensations 16 

The  Intensity  of  Sensation  and  the  Intensity  of  the  Stimulus  ...  20 

Haptic  Sensations  and  Dermal  Pain 24 

The  Quality  and  Intensity  of  Sensation 27 


CHAPTER    III. 

The   Discrimination  of  Weights   without  Effort    and   the   Intensity  of 

the  Stimulus. 


Sec. 

I. 

Sec. 

2. 

Sec. 

3- 

Sec. 

4- 

Sec. 

5- 

Preceding  Investigations 

Further  Experiments :    Method  of  Procedure 

Results 

The  Constant  Error 

The  Confidence  of   the  Observer 


29 
31 
38 
43 
44 


IV  CONTENTS. 

CHAPTER   IV. 
The  Place  of  Stimulation. 

Sec.  I.  Previous  Investigations 

Sec.  2.  Further  Experiments :    the  Accuracy  of  Discrimination 

Sec.  3.  The  Intensity  of  the  Sensation 

Sec.  4.  The  Threshold  for  Pain 

CHAPTER   V. 

Sensations  of  Impact. 

Sec.  I.  The  Threshold  for  Touch 

Sec.  2.  The  Threshold  for  Pain 

Sec.  3.  The  Analysis  of  Mass  and  Velocity  in  Impact  Stimuli 

Sec.  4.  The  Discrimination  of  Mass  and  Velocity 

CHAPTER  VI. 
The  Area  of  Stimulation. 

Sec.  I.  The  Area  of  Stimulation  and  Judgments  of  the  Intensity  of  the 
Stimulus 

Sec.   2.     The  Threshold  for  Touch 

Sec.   3.     The  Threshold  for  Pain 

Sec.  4.  Theoretic  Interpretation  of  Experiments  on  the  Intensive  Effect  of 
the  Area   ...  

Sec.   5.     The  Area  and  the  Discrimination  of  Intensity 

Sec.   6.     The  Intensity  of  Stimulation  and  the  Discrimination  of  Areas    .    . 

CHAPTER   VII. 

The  Time  of  Stimulation. 

Sec.   I.     The  Intensity  of  Haptic  Sensations  in  Relation  to  the  Time  ;   Low 

Intensities 

Sec.   2.      High  Intensities 

Summary       


INTRODUCTION. 

The  extent  to  which  mental  phenomena  can  be  measured 
is  not  the  least  important  of  the  many  problems  before 
Experimental  Psychology.  If  one  mental  process  is  func- 
tionally related  to  another,  it  is  possible  for  Psychology  to 
become  an  exact  science.  If,  however,  the  only  measurable 
attribute  of  Mind  is  Time,  Psychology  can  never  hope  to 
attain  to  the  exactness  of  the  physical  sciences. 

The  solution  of  this  problem  will  be  found  only  by  expe- 
rience. The  psychologist  should  not,  moreover,  be  dis- 
couraged because  Herbart's  heroic  attempt  to  apply  to  Psy- 
chology the  methods  of  Mechanics  was  an  ultimate  failure, 
nor  yet  because  Fechner's  famous  logarithmic  law  is  not 
now  generally  accepted.  Even  if  the  measurement  of  men- 
tal relations  be  yet  an  open  question,  exact  methods  may  be 
applied  to  the  investigation  of  the  subjective  correlatives  of 
measurable  physical  phenomena.  The  most  obvious  prob- 
lem of  the  kind  is  the  relation  between  the  intensity  of 
stimulation  and  the  corresponding  sensation.  But  stimuli 
may  vary  in  the  time  and  area  of  application  as  well  as  in 
the  intensity.  If  intensity  be  a  measurable  attribute  of  sen- 
sation, and  if  the  time  and  area  of  stimulation  be  also  related 
to  the  intensity  of  sensation,  the  relation  of  the  four  quan- 
tities may  be  expressed  in  the  form  of  an  equation : 

S  =/{i,  a,  t). 

Only  when  such  an  equation  is  determined  will  the  foun- 
dation be  laid  for  the  mathematical  investigation  of  mental 
phenomena.  For  it  is  doubtful  if  exact  methods  can  be 
applied  to  the  study  of  mental  relations,  independent  of 
physical  phenomena,  until  the  much  simpler  problems  of 
Psycho-physics  have  been  solved. 


2  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

In  the  following  pages  we  will  discuss  systematically  the 
relations  existing  between  the  intensity,  area  and  time  of 
dermal  stimuli,  and  the  resultant  sensations  and  perceptions. 
We  will  first,  however,  treat  of  dermal  sensations  with  refer- 
ence to  the  quality  of  the  stimulus.  In  this  way  we  shall 
be  in  a  position  to  appreciate  more  fully  the  significance  of 
the  effects  of  variations  of  the  stimulus  in  quantity. 


CHAPTER  I. 

Dermal  Sensations  and  the  Quality  of  the  Stimulus. 

Sec.  I.   Semi-Organic  Sensations  and  their  Stimuli. 

Unlike  the  end-organs  of  the  other  senses,  that  of  touch 
shows  traces  of  the  primitive  sensibility  of  the  entire  peri- 
phery. Instead  of  being  specialized  in  structure  and  func- 
tion, the  skin  has  many  different  and  independent  functions. 
Even  its  sensory  functions  are  quite  distinct.  Not  only  are 
tactile  and  temperature  sensations  utterly  disparate,  but 
equally  distinct  are  many  obscure  sensations  which,  though 
apparently  of  dermal  origin,  seem  allied  in  their  vagueness 
and  diffusiveness  rather  to  the  group  of  general  or  organic 
sensations.  These  may  be  called  semi-organic  sensations, 
since  they  represent  the  transition  stage  from  those  sensa- 
tions which  refer  to  the  outer  world  and  those  which  refer 
only  to  the  activities  of  the  organism.  Nevertheless,  we. 
are  not  justified  in  considering  all  dermal  sensations  as  mem- 
bers of  the  organic  group,  as  has  been  attempted  by  some. 
For  temperature  and  pressure  sensations  are  clearly  the 
data  for  cognitions  of  the  environment  and  not  of  the  activi- 
ties of  the  organism. 

In  the  case  of  many  of  these  sensations  the  stimuli  are 
clearly  some  peripheral  or  other  physiological  processes  in- 
dependent of  external  agency.  Where  the  sensation  appears 
to  be  induced  by  external  stimulus,  physiologists  have  en- 
deavored to  explain  the  quality  of  the  sensation  by  interme- 
diate processes  which  are  considered  the  true  stimuli  in 
such  sensations.  Among  such  processes  are  irradiation, 
summation,  vaso-motor  disturbances,  and  sympathetic  ner- 
vous action.  The  resultant  Mitempfindungen  are  considered 
as  the   subjective   effects  of  heterogeneous  sensory  excita- 

3 


4  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

tions.^  In  the  case  of  the  tickle  sensation,  however,  which  is 
induced  only  by  external  pressure,  such  pressure  must  be 
considered  as  the  stimulus,  since  it  is  the  physical  ante- 
cedent of  a  sensation.  The  intermediate  neural  processes 
may  not,  moreover,  contribute  so  much  to  the  quality  of  the 
sensation  as  may  functional  peculiarities  of  sensory  cells. 
According  to  Bronson,  indeed,  the  tickle  sensation  is  a  relic 
of  a  primitive  contact  sense  which  existed  long  before  touch 
proper,  and  which  is,  therefore,  closely  related  to  the  activi- 
ties of  self-preservation  and  reproduction.^ 

Another  state  of  consciousness,  frequently  of  dermal  ori- 
gin, is  pain.  If  pain  be  a  sensation,  it  must  belong  to  the 
organic  or  semi-organic  group ;  and,  in  fact,  is  so  classified 
by  Weber,  Funke,  Wundt  and  others.^  As  it  is  not  claimed 
that  dermal  pain  is  caused  only  by  secondary  nervous  exci- 
tations, its  relation  to  the  stimulus  will  be  discussed  in  an- 
other chapter. 

Sec.  2.   Se?isations  of  Touch  and  Temperature. 

In  spite  of  the  universal  agreement  that  the  tactile  and 
temperature  senses  are  utterly  disparate,  it  has  been  claimed 
on  experimental  grounds  that  sensations  of  touch  and  temper- 
ature are  causally  related.  Weber  found  that  a  cold  coin  was 
judged  heavier  than  a  warm  one;*  and  Szabadfoldi  found, 
conversely,  that  a  hot  wooden  cylinder  seemed  heavier  than 
one  of  the  temperature  of  the  skin.^  Szabadfoldi  experi- 
mented only  on  himself;  but  Weber's  experiments  were 
conclusive,  and  have  been  corroborated  by  Dessoir."  This 
writer  questions  Szabadfoldi's  results,  but  we  have  con- 
firmed them  in  the  following  manner: 

^Quincke,  Zeit.  fur  Klin.  Med.,  Bd.  xvii.  1890,  429  ;  Goldscheider,  Berlin. 
Physiol.  Gesell.,  1890-91,  no.  i,  5  ;  Kiilpe,  Grundriss  der  Psy.,  92  ;  Wundt,  Grund- 
zuge  der  Phys.  Psy.,  iv.**  Auf.,  I,  408  ;  Dessoir,  Archiv.  fur  Anat.  und  Physiol., 
1892,  324. 

^Bronson,  The  Medical  Record,  xxviii.  425. 

'Weber,  Wagner s  Handbuch  der  Physiol.,  iii.  2*®  Abth.  ;  Funke,  Hermann' t 
Physiologic,  iii.  292  ;  Wundt,  op.  cit. ,  i.  544. 

*  Weber,  op.  cit.,  512. 

^  Szabadfoldi,  Moleschotf s  Untersuchungen,  IX,  624. 

*  Dessoir,  op.  cit.,  305. 


DERMAL  SENSATIONS— QUALITIES  OF  THE  STIMULUS.        5 

A  25-cent  silver  coin  was  heated  in  water  to  a  tempera- 
ture of  from  50°  to  55°  C,  and  then  placed  carefully  upon 
the  palm  of  the  observer's  hand,  the  eyes  being  closed.  It 
was  then  removed,  and  a  similar  coin  heated  to  about  the 
temperature  of  the  skin  was  placed  upon  the  hand.  This 
was  repeated  a  number  of  times,  though  occasionally  the  hot 
stimulus  was  the  second  to  be  applied.  Four  observers 
judged  the  hot  coin  heavier,  and  one  showed  no  marked 
constant  tendency.  With  one  observer  the  writer  applied 
two  coins  simultaneously,  one  over  the  other,  the  pressure 
of  the  two  being  compared  with  that  of  the  hot  coin.  The 
one  hot  coin  was  judged  heavier  five  times  in  ten  trials^ 
some  of  the  observer's  answers  being  guesses.  From  these 
experiments  we  conclude  that  pressure  stimuli  of  low  inten- 
sity and  high  temperature  are  judged  heavier  than  those 
having  the  temperature  of  the  skin. 

It  does  not  follow,  however,  that  all  stimuli  thus  differing 
in  temperature  will  give  rise  to  such  illusions.  In  order  to 
ascertain  whether  hot  or  cold  weights  of  high  intensity  are 
judged  heavier,  the  writer  applied  to  the  palm  of  the  hand 
a  brass  kilogram  weight  heated  to  about  50°  C.  This  was 
removed  and  placed  again  upon  the  hand,  but  not  in  contact, 
a  circular  card-board  of  the  area  of  the  base  lying  between 
the  weight  and  the  skin.  The  hand  of  the  observer  was 
comfortably  supported.  Different  persons  served  as  sub- 
jects, and  all  were  ignorant  of  the  purpose  of  the  experiment. 
As  in  the  preceding  experiment,  a  number  of  trials  were 
made  for  each  observer.  Similar  experiments  were  made 
with  a  cold  weight  and  one  which  had  no  appreciable  tem- 
perature effect  on  the  skin.  The  cold  weight  generally  had 
a  temperature  equal  to  that  of  the  room,  about  20°  C,  and 
at  times  much  below  this,  so  that  from  the  area  of  stimula- 
tion, 16  sq.  cm.,  and  the  conductivity  of  the  metal,  a  marked 
sensation  of  cold  was  produced.  It  was  found,  as  shown  in 
the  table  of  results  given  below,  that  stimuli  of  very  high  or 
low  temperature  are  not  judged  heavier  at  1000  g.  In  fact, 
the  hot  weight  is  rather  judged  lighter.  In  the  table  here 
given  the  figures  denote  the  number  of  times  the  cold  and 


*6 


SENSATIONS  FROM  PRESSURE  AND  IMPACT. 


liot  weights  were  judged  heavier  or  lighter  than   those  of 
%noderate  temperature. 


1 

Cold  weight,  i  kg      i      Hot  weight,  i  kg 

_ 

Observer. 

Heavier.      Lighter.   , 

Heavier. 

Lighter. 

L.  F. 

S.  F. 
K. 

M.  G. 
J.  G. 

2 

2 
7 

5 

6 

3 
3 

5 

2 
0 
2 
4 
4 

8 
10 

5 
6 
6 

Total, 

i6                  17         ij         12 

1 1 

35 

The  results  above  given  go  to  show  that  tactile  and  tem- 
perature sensations  are  not  related,  as  Weber^  and  Szabad- 
■foldi^  inferred.  Dessoir's  explanation  is  that  the  illusion  is 
due  to  the  contraction  of  the  skin  from  the  lower  tempera- 
ture, and  consequent  increase  in  the  number  of  sensory- 
nerves  that  are  affected.^  But  heated  coins  are  overesti- 
mated, and  according  to  this  hypothesis  they  should  be 
underestimated.  A  more  satisfactory  explanation  is  that  an 
illusion  of  judgment  is  involved.^  This  is  rendered  plausible 
by  the  fact  that  stimuli  of  high  intensities  are  not  over- 
estimated. We  may  suppose  that  the  mind  tends  to  infer 
from  the  intensity  of  the  temperature  sensation  that  the 
corresponding  stimulus  is  of  greater  magnitude,  and  there- 
fore heavier  than  the  stimulus  causing  a  purely  haptic^ 
sensation  of  but  little  intensity.  For  heavy  weights  we 
should  on  this  hypothesis  expect  underestimation  rather  than 
overestimation,  of  hot  or  cold  stimuli,  and  that  there  is  some 
such  tendency,  at  least  for  hot  weights,  the  experiments 
seem  to  show.  The  objection  of  Dessoir  against  such  an 
explanation  is,  we  think,  inconclusive.     A  difference  in  dis- 

^  Weber,  op.  cit.,  551. 
'  Szabadfoldi,  op.  cit. 
'  Dessoir,  op.  cit.,  306. 
*  €f.  Funke,  op.  cit.,  321. 

'  We  use  the   term   haptic  (Greek   dTrTd.ofj.aL)  of    all  sensations  of  contact,  touch, 
pressure  or  impact.     For  this  term  we  are  indebted  to  Dessoir. 


DERMAL  SENSATIONS— QUALITIES  OF  THE  STIMULUS.        / 

crimination-time  for  weight  and  temperature  when  only  the 
quantity  judged  is  variable,  does  not  preclude  such  an  illu- 
sion when  the  conditions  are  different. 

The  other  experimental  evidence  in  favor  of  any  funda- 
mental relation  between  haptic  and  temperature  sensations 
is  equally  inconclusive.  The  fact  that  heavy  weights  seem 
hotter  or  colder  than  lighter  weights,  as  stated  by  Noth- 
nagel,^  may  be  due  to  differences  in  conduction  arising  from 
differences  in  contact.  Wunderli  found  that  observers  had 
difficulty  in  distinguishing  tactile  from  temperature  stimuli 
of  low  intensity.^  But  the  errors  occurred  only  when  the 
back  was  the  surface  stimulated,  and  though  temperature 
stimuli  were  confused  with  tactile  stimuli,  the  reverse  error 
did  not  occur.  As  we  are  not  accustomed  to  temperature 
sensations  in  the  back,  such  a  confusion  is  but  natural,  espe- 
cially when  the  stimuli  are  of  such  low  intensity  that  the 
process  of  perception  is  obscured. 

Sec.  3.  Active    Touch. 

The  great  majority  of  so-called  tactile  sensations  are  in 
reality  results  of  complex  kinaesthetic  and  haptic  sensory 
elements.  In  fact,  many  have  distinguished  between  active 
and  passive  touch.  Dessoir  opposes  contact  sensations  to 
those  of  pselaphesia,^  and  Bronson  goes  so  far  as  to  consider 
contact  sensations  and  those  of  active  touch  not  only  as  quite 
distinct  but  as  having  different  end  organs.*  It  is  clear, 
however,  that  active  touch  may  involve  movement  with  or 
without  muscular  effort,  or,  conversely,  muscular  effort  with 
or  without  movement.  We  have,  therefore,  a  triple  set  of 
sensory  impulses  to  consider  as  the  physiological  antecedents 
of  the  sensation  of  active  touch. 

Many  psychologists  have  explained  the  sensation  of  move- 
ment by  alterations  in  the  tension  of  the  skin  and  by  atmos- 
pheric   pressure.^      This    view    is    apparently    corroborated 

^  Nothnagel,  Deutsches  Archiv.  fiir  Klin.  Med.,  II,  298. 
'  Wunderli,  Moleschotf  s  Untersuchungen,  VII,  393. 
'Dessoir,  op.  cit.,  242. 
*  Bronson,  op.  cit. 

*For  references  see  the  works  of  Wundt  and  James,  and  Delabarre,  Ueher  Be- 
'wegungse77ipfindungen,  Freiburg,  1891. 


8  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

by  the  influence  of  dermal  anaesthesia  or  hyperaesthesia 
on  the  perception  of  movement.  The  pathological  evidence 
proves  that  dermal  sensations  enter  into  those  of  movement, 
but  that  is  all.  Other  well  authenticated  observations  show 
that  anaesthesia  does  not  necessarily  affect  the  perception  of 
movement.  In  complexes  of  tactile  and  kinaesthetic  sensa- 
tions we  must,  therefore,  assume  different  sensory  processes. 
But  active  touch  is  possible  without  movement  either  of 
the  stimulus  or  the  sense  organ.  If  through  an  act  of 
volition  we  exert  pressure  upon  an  external  object,  we  have 
in  addition  to  the  sensation  of  dermal  pressure  that  of  effort. 
In  fact,  all  the  feelings  of  strain  and  tension  are  felt  which 
enter  into  the  muscular  consciousness.  As  pathological  ob- 
servations and  experiments  on  lifted  weights  prove  the 
muscular  sense  to  be  independent  of  touch, ^  it  is  evident  that 
where  pressure  is  exerted  voluntarily  the  resultant  sensation 
is  complex,  and  not  a  haptic  sensation  proper.  We  have, 
therefore,  to  distinguish  between  what  we  might  call  subjec- 
tive pressure,  or  pressure  with  effort,  and  objective  pressure, 
or  pressure  without  effort. 

Sec.  4.   Passive  Touch. 

Having  analysed  the  various  elements  entering  into  tactile 
complexes,  we  turn  to  those  sensations  in  which  the  subject 
is  passive  and  the  stimulus  acts  only  upon  a  definite  area. 
The  stimulus  may  then  be  pressure  exerted  upon  the  skin, 
the  energy  of  a  body  striking  the  skin,  or  traction  tending 
to  separate  the  dermal  end  organ  from  the  organism  to  which 
it  belongs.  These  stimuli  are  qualitatively  different,  as  are 
the  corresponding  sensations,  though  for  traction  these  are 
less  distinct  than  would  be  supposed. ^  The  blow  of  a  mov- 
ing object  upon  the  periphery  gives  rise  to  a  sensation  dis- 
tinct from  that  of  a  motionless  weight.  This  difference 
increases  with  the  velocity  of  the  moving  mass.  The  stim- 
ulus in  such  sensations,  therefore,  is  to  be  considered  the 
product  of  the  mass  and  its  velocity,  or  some  function  of  its 
velocity.  The  resulting  sensation  may  be  called  a  sensation 
of  impact,  as  distinguished  from  one  of  pressure. 

^See  Wundt,  op.  cit.,  i^ii;  Delabarre,  op.  cit.,  37,  38. 
'See  Hall  and  Motora,  Am.  Journal  of  Psy.,  I,  72. 


DERMAL  SENSATIONS— QUALITIES  OF  THE  STIMULUS.         9 

But  is  not  this  difference  between  pressure  and  impact 
only  a  difference  in  degree?  When  a  weight  is  applied  to 
the  hand  there  must  be  some  impact,  whatever  be  the  veloc- 
ity at  which  the  weight  be  applied.  If  a  weight  of  low 
intensity,  as  loog  or  less,  be  applied,  and  the  area  of  stimu- 
lation be  not  too  small,  the  sensation  is  one  of  impact ;  but  if 
a  stimulus  of  moderate  intensity  be  used,  a  distinct  pressure 
sensation  will  be  observed  in  addition  to  that  of  impact. 
This  is  due  to  the  effect  of  the  weight  in  overcoming  the 
elasticity  of  the  skin  and  depressing  the  dermal  tissues.  The 
stimulus  in  pressure  sensations  may,  therefore,  be  considered 
not  momentum  or  kinetic  energy,  but  rather  as  mechanical 
force  exerted  through  the  object  in  contact  with  the  skin,  or 
more  accurately,  the  work  done  by  this  force  in  displacing 
the  dermal  tissues.  In  reality,  however,  the  process  of 
stimulation  is  often  more  complex.  When  the-  pressure  is 
sufficiently  great  to  produce  motion,  kinaesthetic  elements 
will  affect  the  sensory  result.  When  movement  is  prevented 
by  opposing  forces,  a  double  process  of  dermal  stimulation 
will  result,  since  action  and  reaction  are  equal  and  opposite. 

Sec.  5.    The  Classification  of  Dermal  Sensations. 

The  general  results  of  the  analysis  above  given  may  be 
summarized  in  a  classification  of  dermal  sensations  with 
special  reference  to  the  quality  of  the  stimulus : 


Dermal 
Sensations  " 


Simple,  or 
Purely  Dermal 


Compound, 
or 
Semi-Dermal 


Haptic 


-<     Temperature 


Semi-orgfanic 


Subjective 
Pressure 


Kinaesthetic 


i  Traction. 

\  Objective  pressure. 

(  Impact. 

j  Heat. 
■  Cold. 

Tickle. 

Itching. 

Creeping. 

Pain. 

With 

movement. 

Without 

movement. 

With  effort. 

Without 
effort. 


CHAPTER   II. 

The  Intensity  of  Stimulation. 

Sec.  I.    The  Concept  Intensity. 

The  term  intensit}^  as  applied  to  neural  stimuli,  has  long 
been  in  universal  use  among  psychologists,  but  frequently  in 
a  manner  that  is  far  from  exact.  In  physical  science  the 
term  is  used  as  the  quantitative  predicate  of  force.  But 
many  stimuli,  as  those  of  smell  and  taste,  cannot  be  meas- 
ured in  terms  of  force.  To  avoid  ambiguity  in  the  use  of 
this  term,  we  would  suggest  as  a  working  definition  of  in- 
tensity, as  used  in  Psychology,  the  following,  which  is  based 
upon  obvious  psychological  grounds :  that  quantitative  prop- 
erty of  neural  stimuli,  the  magnitude  of  which  determines 
whether  or  not  they  give  rise  to  a  sensation ;  and,  if  so, 
whether  that  sensation  be  painful,  or  have  only  the  particu- 
lar quality  due  to  the  quality  of  the  stimulus. 

From  this  point  of  view  the  intensitv  of  visual  and  audi- 
tory stimuli  ma}^  be  measured  by  the  energy  of  motion 
transmitted  to  the  end  organ  in  a  given  time.  The  inten- 
sity of  gustator}^  and  olfactory  stimuli  may  be  measured  for 
a  given  substance  by  the  quantity  which  is  applied  to  the 
end  organ.  But  with  temperature  stimuli  the  measure  of 
intensity  is  more  complex.  Then,  too,  as  heat  and  cold  are 
physically  the  same,  the  absolute  measure. of  heat  is  not  the 
measure  of  the  intensity  of  heat,  as  regards  its  physiological 
and  psychological  effects.  Passing  from  the  temperature 
sense  to  that  of  effort,  the  work  done  by  muscular  contrac- 
tion in  a  given  time  is  clearl}-  the  measure  of  intensity ;  but 
when  no  motion  takes  place  the  criterion  is  different,  as 
such  units  cannot  be  used.  In  this  case  the  measure  of  in- 
tensity is  clearly  the  force  which  is  exerted. 

The  measurement  of  the  intensity  of  haptic  stimuli  is, 
fortunately  for  our  purpose,  comparatively  simple.      When 

lO 


THE  INTENSITY  OF  STIMULA  TION.  1 1 

impact  may  be  neglected,  the  intensity  of  the  stimulus  is 
measured  by  the  weight  that  is  applied ;  for  the  work  done 
in  depressing  and  displacing  the  dermal  tissues  will  be  pro- 
portionate to  the  impressed  force.  When,  however,  appre- 
ciable movement  occurs  before  the  full  pressure  is  exerted, 
the  matter  is  more  complex,  since  the  subjective  effect  is 
dependent  not  only  on  the  mass  but  also  on  its  velocity. 
We  might  suppose  that  the  measure  of  the  intensity  of  an 
impact  stimulus  would  be  the  product  of  the  mass  and  the 
square  of  the  velocity,  since  this  quantity  represents  the 
energy  of  the  blow.  But,  as  we  shall  find  in  the  chapter  on 
Sensations  of  Impact,  the  square  of  the  velocity  does  not 
appear  to  have  as  intensive  an  effect  as  does  the  mass. 

Sec.  2.    Touch  and  Pressure. 

It  was  shown  by  Aubert  and  Kammler  that  pressure  and 
impact  stimuli,  below  a  certain  intensity,  are  not  perceived.^ 
The  sensations  from  stimuli  of  low  intensity  are  sensations 
of  passive  touch,  the  element  of  pressure  being  apparently 
absent.  From  such  data  Meissner  inferred  that  pressure 
sensations  are  absolutely  distinct  from  those  of  touch  proper, 
emfache  Tas  temp  find ungen,  and  that  these  have  special  end 
organs,  the  tactile  corpuscles.^  Meissner's  distinction  be- 
tween touch  and  pressure  is  accepted  by  Aubert  and  Kamm- 
ler, Bronson  and  Dessoir,  but  is  rejected  by  Funke,  Wundt 
and  Kiilpe.  We  shall  now  consider  in  detail  the  evidence 
that  has  been  brought  forward  to  support  this  view. 

According  to  Meissner,  touch  furnishes  the  data  for  the 
concept  of  externality,  and  accompanies  all  pressure  sensa- 
tions, though  not  necessarily  accompanied  by  them.^  Clearly, 
however,  this  is  but  an  hypothesis  to  account  for  what  is 
assumed,  that  is,  the  difference  between  touch  and  pressure. 
Aubert  and  Kammler  reject  Meissner's  hypothesis,  basing 
their  distinction  upon  their  alleged  observation  that  contact 
sensations  are  subjective  modalities.     This  does  not  accord 

^  Aubert  and  Kammler,  Molesckotfs  Untersuchungen,  v.  145. 
''Meissner,   Zeitschrift  fur  Rat.  Med.,  2*^  R.,  iv.  ;  also,  Beitrage  zur  Anatomic 
und  Physiol,  der  Haut,  Leipzig,  1853. 
^Meissner,  op.  cit.,  212. 


12  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

with  the  introspection  of  the  writer.  The  apparent  differ- 
ence observed  may  be  due  to  the  fact  that  stimuli  of  low 
intensity  do  not  give  rise  to  sensations  of  sufficient  clearness, 
for  the  mind  to  perceive  the  quality  of  the  stimulus.  We: 
certainly  do  refer  a  tactile  sensation  to  an  external  somethings 
though  what  that  may  be  we  may  not  know. 

Dessoir  gives  as  the  characteristic  of  pressure  sensations, 
the  feeling  of  effort  which  is  involved.^  But  Dessoir  un- 
doubtedly refers  to  subjective  pressure,  or  pressure  with 
effort;  and  as  sensations  of  pressure  are  possible  without 
effort,  the  criterion  is  not  applicable. 

Bronson  bases  his  separation  from  pure  contact  of  psela- 
phesia,  or  perceptive  touch,  partly  upon  the  above  facts  of 
introspection  and  partly  upon  the  apparent  relationship  of 
sensations  of  contact  to  semi-organic  sensations.^  Accord- 
ing to  Bronson,  sensations  of  contact  require  as  their  peri- 
pheral antecedents  only  the  stimulation  of  the  epidermal 
fibrillas,  and  are,  therefore,  to  be  considered  distinct  and 
primitive  sensations. 

However  conclusive  be  Bronson's  arguments  as  to  the 
biological  theory  of  dermal  sensations,  they  do  not  prove' 
touch  to  be  distinct  from  pressure,  because  the  tickle  sensa- 
tion does  not  necessarily  accompany  that  of  contact.  It  is- 
a  distinct  state  of  consciousness  independent  of  the  tactile 
sensation,  and  the  same  may  be  said  of  the  aphrodisiac  sense.. 
We  conclude,  therefore,  that  there  is  no  psychological  basis; 
for  the  distinction,  unless  there  be  other  evidence  than  that: 
which  we  have  discussed.  If  touch  and  pressure  were  dis- 
tinct, we  should  look  for  such  evidence  in  pathology ;  but 
the  writer  knows  of  none.  Bronson  states  that  hyperaes- 
thesia  and  apselaphesia  may  coexist.  But  it  is  probable  that 
he  really  refers  to  hyperalgesia,  which  is  quite  irrelevant. 
According  to  Richet,  tactile  hyperaesthesia  is  unknown. 3- 
There  have  been  instances  of  anaesthesia  for  pressure  stimuli 
of  low  intensity  without  anaesthesia  for  those  of  high  inten- 

^  Dessoir,  op.  cit. ,  242. 

*  Bronson,  o/>.  cit.     Bronson  does  not  state  these  arguments  categorically,  but  the: 
above  appears  to  be  his  position. 

'Richet,  Richer ches  sur  la  Sensibility,  219. 


THE  INTENSITY  OF  STIMULATION.  1 3 

-sity.^  But,  as  Richet  observes,  this  may  be  explained  by 
the  fact  that  the  nerves  die  first  at  their  extremities. 

Apart,  however,  from  these  negative  considerations,  it 
must  be  admitted  that  the  classification  of  one  group  of  sen- 
sations, as  distinct  from  another  group,  logically  implies  our 
inability  in  introspection  to  pass  gradually  from  one  to  the 
other.  By  this  criterion  the  sense  of  touch  and  that  of 
pressure  must  be  identical.  It  is  impossible  to  tell  where 
one  begins  and  the  other  ends.  Stimuli  that  are  barely  per- 
ceptible may  be  judged  with  reference  to  their  weight.^  On 
the  other  hand,  individuals  differ  as  to  what  they  call  pres- 
sure. In  the  course  of  experiments  on  the  threshold  of 
pain,  to  be  described  in  the  next  section,  one  observer  said 
he  began  to  feel  pressure  at  3.5k.,  pain  appearing  at  8.5k. 
The  writer  would  call  that  sensation  one  of  pressure  when 
the  instrument  used  registered  only  i.ok. 

Even  if  touch  and  pressure  be  indistinguishable,  the  ap- 
parent change  of  quality  requires  an  explanation.  That 
generally  given  is  that  different  physiological  processes  are 
induced  by  intense  stimuli.  Aubert  and  Kammler  explain 
the  distinction  by  the  displacement  of  the  skin.  But  this  dis- 
placement varies  with  the  intensity  of  the  stimulus.^  Kiilpe 
mentions  the  effect  of  intense  pressure  upon  the  muscular 
tissues,*  but  we  have  pressure  sensations  where  there  are  no 
muscles.  Meissner's  hypothesis,  to  which  that  of  Bronson 
is  similar,  that  the  sensory  cells  in  the  dermis  are  the  ana- 
tomical basis  of  pressure  sensations,  is  inadequate,  since 
these  cells  appear  to  be  absent  on  parts  that  are  sensitive  to 
pressure.^  Goldscheider  found  special  pressure  spots, ^  but 
his  results,  both  histological  and  psychological,  are  dis- 
puted.^ The  writer's  own  observation  does  not  enable  him 
to  detect  the  existence  of  points  that  give  pressure  or  con- 
tact sensations  only.     Certain  spots  may  be  more  sensitive 

^Richet,  op.  cit.,  227. 

'See  Chapter  III.,  Section  3. 

*  For  measurements  of  this,  see  Hall  and  Motora,  op.  cit. 

*  Kiilpe,  op.  cit.,  91. 

^Cf.  Wundt,  op.  cit.,  i.  302  ;  Dessoir,  op.  cit.,  275. 

•Goldscheider,  Archiv.  fur  Anat,  und Physiol.,  1885  Supp.  Bd.,  76. 

^Cf.  Dessoir,  op.  cit.,  251. 


14 


SENSATIO.VS  FROM  PRESSURE  AND  IMPACT. 


than  others,  but  this  would  throw  no  light  on  the  question^ 
Besides,  it  is  difficult  to  obtain  a  distinct  sensation  of  pres- 
sure when  so  small  an  area  is  stimulated  as  is  necessary  in 
such  experiments,  since  the  sensation  of  pressure  passes  sq 
quickly  into  that  of  pain  or  other  semi-organic  sensations. 

But  if  there  is  no  additional  process  of  sensory  excita- 
tion in  pressure  sensations,  in  what  way  may  the  apparent 
difference  be  explained?  Our  answer  is  that  there  is  no  dif- 
ference in  sensation,  but  only  in  perception.  What  we 
mean  by  a  sensation  of  pressure  is  one  of  such  a  quality  that 
we  can  ascribe  the  subjective  effect  to  some  definite  objective 
cause  and  one  exerting  such  pressure  that  its  removal  would 
involve  appreciable  muscular  work.  The  apparent  differ- 
ence may,  we  think,  be  thus  explained,  for  it  is  impossible  to 
analyse  in  consciousness  the  mental  reaction  in  perception 
out  oi  the  total  sensational  and  perceptive  complex. 

3.    The  Threshold  of  Pam. 

For  the  purpose  of  measuring  the  intensity  of  pressure 
causing   pain   a   spring    dynamometer    was    used    by   which 
a    given    pressure    could    be    exerted    upon     an}^    surface.-^ 
Attached    to    the    lower    end    of    the  spring 
was  a     sliding    cylindrical    piece     of    brass. 
This    was    capped     with    hard     rubber    (A), 
which    was    applied    to    the     surface    to     be 
stimulated.     The    cap    which    came    in    con- 
tact   with    the    skin    was    hemispherical,    and 
about  8mm.   in  diameter.     The  pressure  was 
exerted    by    the    hand  of    the    experimenter, 
and  the  amount  of    pressure    was    registered 
in     kilograms     by    the     movable     piece     (B) 
attached     to     the     spring.      The     scale     was 
tested    by    an    accurate    balance    adapted    to 
heavy    weights,    and    was    found    to    be    free 
from    appreciable    error.     The  stimulus    was 
applied    by   the  writer  to    the    volar   surface 
of    the    left    hand    of    the    subject     over     the     fifth     meta- 

^  This  instrument  was  devised  bj'  Prof.  J.  !McK.  Cattail.     He  has  suggested  the 
term  algometer  by  which  to  designate  it,  and  this  expression  will  be  used  hereafter. 


Fig.  I. 


A 


U 


THE  INTENSITY  OF  STIMULATION. 


15; 


carpal.  The  pressure  was  increased  as  nearly  as  possible 
at  the  same  rate  for  dilTerent  observers,  about  1.4k.  per 
sec.  If  we  take  .3  sec.^  as  the  double  reaction-time,  we 
have  to  subtract  i.4X.3=.4k.  from  the  reading  of  the  instru- 
ment. The  observers  were  asked  to  speak  when  the  in- 
strument began  to  hurt  at  all  or  be  uncomfortable  ;  for  it  was 
found  that  individuals  differed  as  to  what  they  called  'pain.' 
The  subjects  tested  were  students  in  Columbia  and  Barnard 
Colleges  and  in  private  schools.^  Below  we  give  the  average 
in  kilograms  as  well  as  the  maxima  and  minima  corrected  for 
the  constant  error  above  referred  to.  The  approximate  ages 
a,re  also  given. 


Ob- 
servers. 

50  Boys. 

40  College 

Students. 

(Men.) 

38  Law 
Students. 

58 
Women. 

40  College 
Students. 
(Women.) 

Ages, 

12  to  15 

16  to  21 

19  to  25 

16  to  20 

17  to  22 

Av., 

4.8 

5-1 

7.8 

Z-^ 

3.6 

Max., 

8.4 

13.6 

15  + 

7.6 

8.6 

Min., 

2.1 

1.9 

3-9 

1.8 

1-7 

From  the  above  results  it  appears  that  although  individu- 
als differ  greatly  in  sensitiveness  to  pain,  on  the  whole  women, 
and  boys  are  more  sensitive  than  men.  The  variations  in 
those  of  the  same  age  and  sex  are  not  due  to  chance,  since 
any  one  person  when  tested  gives  fairly  constant  results. 
Nor  are  they  due  to  individual  differences  in  perception  and 
judgment,  though  doubtless  these  affect  the  results  to  some 
extent ;  for  it  is  very  easy  to  tell  when  the  pressure  begins 
to  be  uncomfortable,  and  the  '  imagination '  does  not  seem 
to  be  a  disturbing  factor.  Indeed,  the  pain  seems  often  to 
come  with  greater  suddenness.  These  variations  are  rather 
to  be  ascribed  to  constitutional  nervous  differences,  and  in 
part,  perhaps,  to  differences  in  the  thickness  of  the  skin. 


^  This  was  verified  by  chronoscopic  measurements. 

*  The  writer  takes  pleasure  in  acknowledging  his  indebtedness  to  Registrar  Mrs. 
N.  F.  Liggett  and  Principals  Miss  Brown  and  Mr.  Cutler  for  furnishing  him  the 
opportunity  of  making  the  tests  on  young  women  and  boys. 


l6  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

Sec  4.    The  Range  of  Pressure  Sensations. 

If  the  miniimmi  tangible,  or  tactile  threshold  (T),  were 
measurable,  as  is  the  threshold  of  pain  (P),  and  if  the  sensa- 
tion of  pressure  ceased  as  soon  as  that  of  pain  appeared,  we 
could  determine  the  range  of  haptic  sensations  (R)  by  the 

formula:  pi 

R  =  — • 
T 

Since  the  haptic  sensation  does  not  cease  when  pain 
begins,  but  rather  decreases  gradually  as  the  pain  increases, 
the  so-called  range  cannot  be  measured.  We  may,  however, 
use  the  term  to  indicate  the  extent  of  haptic  sensations  up  to 
the  pain  threshold.  But  are  we  justified  in  assuming  the 
pain  threshold  to  be  a  quantity  ?  According  to  the  algedonic^ 
tone  theory  we  are  not  so  justified.  And,  even  assuming 
that  a  stimulus  becomes  painful  at  a  certain  point,  the  one 
.sensation  is  at  first  so  obscured  by  the  other  that  it  is  not  im- 
mediately appreciable.  Nevertheless,  the  appearance  of 
pain  is  generally  so  sudden  when  the  stimulus  is  increasing 
in  intensity,  that  we  treat  the  threshold  of  pain  as  approxi- 
mately a  quantity. 

Assuming  then  that  the  range,  and  therefore  the  thres- 
holds of  touch  and  pain,  can  be  measured,  it  is  evident  that 
in  determining  them  the  conditions  of  stimulation  should  be 
constant.  Not  only  the  time  and  space  conditions,  but  also 
the  mode  of  applying  the  stimulus,  must  be  constant. 

In  the  measurements  of  the  tactile  threshold  made  by 
Aubert  and  Kammler  the  element  of  impact  was  involved,  and 
their  results  could  not  be  compared  with  our  own  measure- 
ments of  the  pain  threshold,  since  in  these  impact  was  ex- 
cluded. Bloch  employed  the  same  method,  that  of  pure 
pressure,^  but  his  experiments  were  made  on  himself,  and 
we  judge  them,  therefore,  inconclusive.  We  found  that  re- 
sults are  obtained  under  such  circumstances  quite  different 
from  those  obtained  when  the  stimulus  is  applied  by  another 

^  Cf.  Wundt,  op.  cit.,  I,  335. 

*  We  have  borrowed  this  translation  of  Gefiihlston  from  Marshall,  Pain,  Pleasure 
.and  Esthetics. 

'Bloch,  Archives  de  Physiologic,  1891,  322. 


THE  INTENSITY  OF  STIMULATION.  1/ 

person  and  the  observer  is  ignorant  of  the  time  of  applica- 
tion. Bloch  gives  .ooo5g  to  .001 5g  as  the  smallest  appre- 
ciable pressure.  Aubert  and  Kammler  found  for  an  area  of 
9mm,  .oo5gas  the  minimum  ta?tgibile.  The  results  above  given 
are  much  more  discordant  than  they  might  at  first  seem, 
since  the  greater  value  for  the  threshold  is  obtained  for  the 
smaller  area/  and  since  impact  is  clearly  involved  rather  than 
pressure.^ 

In  order  to  make  further  experiments  on  the  smallest 
perceptible  haptic  stimuli,  the  writer  constructed  an  instru- 
ment similar  to  that  used  by  Bloch. 

Fig.  2. 


3B 


To  a  wooden  handle  (B)  was  attached  by  wax  a  horizontal 
bristle  (AC),  taken  from  an  ordinary  broom.  At  the  end  (A) 
was  fastened  by  wax  a  vertical  piece  (AD)  of  the  same 
material,  the  point  of  which  was  applied  to  the  part  stimu- 
lated. The  pressure  was  exerted  by  the  hand  of  the  experi- 
menter. The  degree  of  pressure  was  shown  by  the  elevation 
of  the  bristle,  which  was  read  off  on  a  scale  (FK).  The 
readings  on  this  scale  were  in  grams,  the  elevations  corre- 
sponding to  different  pressures  having  been  found  by  a  bal- 
ance. The  pressure  was  applied  upon  a  circular  card  board 
about  .9cm  in  area.  This  card  was  so  light,  .05g,  that  its 
weight  could  be  neglected  after  the  moment  of  application, 
as  it  rested  on  the  skin  during  the  experiments.  The 
observer's  eyes  were  closed,  and  he  did  not  know  when  the 
stimulus  was  applied.  The  rate  of  application  of  the  pres- 
sure was  kept  as  constant  as  possible.  It  was  as  rapid  as 
was  consistent  with  taking  the  readings,  about  .3g  per  sec. 

^  See  chapter  V,  sec.  2. 
*  See  chapter  VI,  sec.  2. 


i8 


SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 


We  subtract,  therefore  .3X.3=-ig  from  the  reading  ob- 
tained. Ten  experiments  were  made  on  S.  F.,  and  also  on 
G.,  the  writer,  for  the  smallest  perceptible  pressure,  T. 
The  same  number  were  made  for  the  threshold  of  pain,  P, 
by  means  of  the  dynamometer  already  described.  The  area 
of  stimulation  for  the  pain  measurements  was  also  .9cm. 
The  results  are  given  in  grams.  The  values  of  the  Range, 
R,  are  found  by  dividing  the  average  values  of  P  by  the 
average  values  of  T. 


Av. 

T. 
Max.  [  Min. 

Av. 

P. 
Max. 

Min. 

P 

R  =  ^ 

T 

F. 
G. 

1.9 
2.6 

2.7 
2.5 

I. 

•4 

3230 
4400 

4300 
5700 

2700 
3800 

1700 
1697 

According  to  these  results  the  haptic  range  is  about  1700. 
The  great  variation  in  the  values  obtained  for  the  thresh- 
old renders  these  figures  necessarily  very  inexact.  The 
values  of  the  threshold  here  given  are  very  much  greater 
than  those  obtained  by  previous  investigations.  The  elimi- 
nation of  the  element  of  impact^  and  of  the  knowledge  of 
the  observer  would  tend  to  give  far  greater  values  than  those 
obtained  by  Bloch  and  by  Aubert  and  Kammler.  Then,  too, 
the  area  and  time  of  stimulation  are  factors  not  to  be  neg- 
lected ;  but  these  differences  are  not  such  as  to  affect  the 
results  appreciably.^ 

It  is  generally  assumed  that  the  threshold  is  a  definite 
quantity.^  In  the  case  of  sensations  of  pain,  the  results 
obtained  for  any  individual  are  sufficiently  constant  to  justify 
this  assumption  as  a  working  hypothesis.  The  results  given 
above  for  the  tactile  threshold  are,  however,  so  variable 
that  we  are  led  to  doubt  the  validity  of  such  an  assumption. 
In  fact,  the  very  conception  of  a  threshold  involves  a  logical 
contradiction.  If  by  this  we  mean  a  quantity  that  we  can 
always   perceive  under    moderately   constant   conditions  of 

^  See  Chapter  V,  Sec.  i. 

»  See  Chapter  VI,  Sec.  2  ;  Chapter  VII,  Sec.  i. 

'  Wundt,  op.  cit.,  I,  334;  Kulpe,  op.  cit.,  51  ;  Ladd,  Elements  of  Phys.  Psy.,  363.. 


THE  INTENSITY  OF  STIMULATION.  I9 

attention,  we  shall  have  to  assume  a  quantity  much  larger 
than  what  we  often  perceive.  In  the  course  of  experiments 
on  the  perception  of  differences  in  weights,  the  application 
of  a  stimulus  of  5g  was  unobserved  several  times,  and  that, 
too,  by  an  excellent  subject,  who  was  expecting  the  stimulus 
at  the  time  of  application.^  Even  a  stimulus  of  loog  has  been 
unobserved  by  good  observers  in  experiments  by  the  method 
of  right  and  wrong  cases.  We  must  conclude,  then,  that 
stimuli  of  a  given  intensity  will  be  observed  a  certain  pro- 
portion of  times  and  no  more,  if  a  sufficient  number  of 
experiments  be  made.  We  may  also  infer  that  stimuli  far 
below  the  so-called  threshold  will  be  observed,  some  times, 
at  least,  in  an  infinite  number  of  trials.  What,  then,  shall 
we  call  the  threshold?  It  is  not  the  quantity  that  is  always 
observed,  for  this  would  involve  a  contradiction.  It  is  not 
that  which  is  observed  a  certain  percentage  of  trials,  for 
this  could  not  be  called  the  least  perceptible  intensity.  We 
can  only  say  that  the  probability  that  a  given  stimulus  will 
be  perceived  by  the  observer  is  functionally  related  to  the 
intensity  of  the  stimulus.  In  fact,  the  so-called  threshold 
is  no  more  a  definite  quantity  than  the  so-called  least  notice- 
able difference,  which  we  think  leads,  when  discussed  from 
the  standpoint  of  probabilities,  to  a  similar  reductio  ad  absur- 
dum}  Indeed,  the  processes  involved  are  much  the  same. 
Not  the  least  important  of  the  factors  entering  into  the 
measurement  of  one  as  well  as  the  other,  is  the  confidence 
of  the  observer,  which  varies  from  extreme  doubt  to  absolute 
certainty.^  The  wrong  cases,  or  mistakes  due  to  errors  of 
observation,  which  occur  when  different  stimuli  are  com- 
pared, have  their  counterpart  in  tactile  hallucinations,  a 
number  of  which  occurred  in  the  course  of  our  experiments 
on  the  threshold.^ 

^  See  Chapter  III,  Sees.  2  and  3. 

'  FuUerton  and  Cattell,  On  the  Perception  of  Small  Differences,  10  ;  Pierce  and 
Jastrow,  National  Academy  of  Sciences,  1884,  III,  75. 
'  See  Chapter  III,  Sec.  5. 
*  Cf.  'K.roh.n,  Journal  of  Mental  and  Nervous  Diseases,  March,  1893,  14. 


20  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

Sec.   5.     The  Intensity  of  Sensation   and  the  Intensity  of  the 
Stimulus. 

This  relation  has  generally  been  investigated  by  deduc- 
tions from  the  relation  of  the  least  noticeable  differences  to 
the  absolute  intensity  of  the  stimulus.  But,  as  is  shown  by 
the  application  of  the  method  of  right  and  wrong  cases,  there 
is  no  such  quantity,  and  therefore  the  deductions  based  upon 
it  are  invalid.  Of  the  other  psycho-physical  methods,  two 
have  been  applied  by  Merkel  to  the  investigation  of  haptic 
sensations.^  By  the  method  of  double  stimuli  it  was  found 
that  the  ratio  of  the  normal  to  the  estimated  double  stimu- 
lus was  approximately  i  :  2  for  from  loog  to  2000g.  By  the 
method  of  mean  gradation  Merkel  found  that  the  values  of 
the  estimated  arithmetic  mean  of  two  stimuli  was  but  slightly 
less  than  the  true  arithmetic  mean.  Merkel's  experiments 
were,  however,  made  only  on  himself,  and  the  muscular 
sense  was  not  excluded,  so  that  his  results  are  not  con- 
clusive. 

In  the  hope  of  throwing  some  light  on  the  much  dis- 
cussed psycho-physical  problem  in  pressure  sensations,  ex- 
periments were  made  by  a  method  different  from  those  gen- 
erally used,  the  observer  being  required  to  judge  of  two 
stimuli  how  much  greater  one  was  than  the  other.  The 
method  of  experiment  in  detail  was  as  follows.  A  wax 
mould  having  been  constructed  to  fit  the  left  hand,  the  hand 
was  placed  in  this,  the  palm  being  upward  under  the  pan  of 
a  balance.  The  pressure  was  given  by  weights  placed  upon 
the  pan  of  the  balance.  The  pressure  was  transmitted  to 
the  hand  by  means  of  a  piece  of  wood  glued  to  the  pan.  A 
circular  cap  of  cardboard  attached  to  the  end  of  the  stick, 
and  about  4  mm  in  diameter,  came  in  contact  with  the  skin. 
The  observer  having  closed  his  eyes,  and  the  cardboard  cap 
being  barely  in  contact  with  the  skin,  a  weight  was  care- 
fully placed  in  the  pan,  and  after  about  two  seconds  was 
removed  and  replaced  by  a  weight  very  much  heavier,  the 
observer  being  asked  to  judge  the  ratio  of  the  weights.  But 
few  experiments  were  made  at  one  sitting,  so  that  memory 

^  Merkel,  Philosophische  Studien,  v.  253. 


THE  INTENSITY  OF  STIMUIA  TION. 


21 


could  not  affect  the  results.  For  purposes  of  convenience 
the  lowest  stimulus  was  applied  first,  the  next  higher  follow- 
ing ;  but  the  reverse  order  was  at  times  adopted  without  per- 
ceptible difference.  The  observers  were,  of  course,  ignor- 
ant of  the  objective  relations  of  the  weights  as  well  as  of 
the  purpose  of  the  experiment.  They  were  all  students  of 
Psychology.  In  the  table  appended  are  given  the  results.. 
The  first  horizontal  column  denotes  the  stimuli  in  grams. 
The  numbers  in  the  vertical  oolumns,  under  those  denoting 
the  stimuli,  indicate  the  average  judgments  as  to  how  many 
times  the  given  stimulus  was  greater  than  the  stimulus  pre- 
ceding. Thus  S.  F.  judged  50  g.,  3.1  times  as  heavy  as  10  g, 
and  2 50 g.,  4.2  times  as  heavy  as  50  g.  The  figures  preceded  by 
the  sign  ±  denote  the  probable  error  of  the  given  average.^ 
But  few  experiments  were  made  on  each  observer,  for 
not  only  were  the  mean  variations  small,  but  the  individual 
differences  were  very  great. 


Observer. 

No.  expts. 

2g- 

10  g. 

50  g. 

250  g. 

1250  g. 

1800  g. 

S.  F. 

10X4 

— 

— 

S.idz.oi 

4.2±.03 

7.i±.04 

3.8±.04 

L.  F. 

6X4 

— 

— 

2.0=b.00 

2.7±.oo 

4.9±.oi 

3.9''zb.oi 

P. 

5X5 

— 

2.2±.00 

2.5zb.OI 

3.o±.oo 

5-6±.03 

3-4i.oi 

K. 

5X5 

— 

i.grh.oo 

i.gdz.oo 

2.I±.00 

3.4zfc.oo 

i.7±.oo 

Av. 

— 



2.0 

2.4 

3-0 

5.2 

3.0' 

In  order  to  represent  the  relation  between  the  stimulus 
and  the  estimate  of  the  stimulus,  let  us  take  the  number  2  as 
representing  the  estimated  weight  at  2  g.  Multiplying  this 
by  the  estimated  values  of  10  g.  in  terms  of  2  g.,  the  number 
obtained  will  represent  the  increase  of  the  estimate  of  the 
stimulus  as  the  stimulus  increases  from  2  to  10.  In  like 
manner,  by  taking  this  result  and  multiplying  it  by  the  esti- 

^  This  is  such  an  error  (or  deviation  from  the  average)  that  half  of  the  errors 
would  be  smaller  and  half  would  be  larger.     It  is  here  obtained  by  the  briefer  formula, 


n  v^n —  I 
See  Merriman,  Airy  and  other  writers  on  the  theory  of  probabilities  and  the  method  of 
least  squares. 

*  This  number  refers  to  2500  g.,  not  to  1800  g.,  as  do  the  others  in  this  column. 

*  This  average  is  based  upon  3  values,  3.8,  3.4  and  1.7.     See  note  i. 


22 


SENSATIONS  FROM  PRESSURE  AND  IMPACT. 


mated  values  of  50  g-.  in  terms  of  10  g.,  we  obtain  the  in- 
crease of  the  estimate  as  the  stimulus  increases  from  10  g. 
to  50  g.  In  the  case  of  S.  F.  and  L.  F.,  as  no  measurements 
were  made  of  the  estimate  of  10  g.  in  terms  of  2  g.,  we  take 
as  the  unit  of  estimated  weight  at  10  g.  4.4,  which  is  the 
value  obtained  for  P.,  with  whose  results  those  of  S.  F.  and 
L.  F.  fairly  agree. ^  In  this  way  the  relative  increase  of 
the  estimate  of  weights  is  obtained.  The  increase  of  the 
stimulus  is  shown  by  the  intensities  used,  these  being,  with 
the  exception  of  the  highest,  in  geometrical  progression. 
Below  are  given  the  calculated  values  of  the  estimates  of  the 
stimuli : 


Observer. 

^g- 

lOg. 

5og. 

250g. 

I250g. 

i8oog. 

S.  F. 

— 

4.4^ 

13- 

57- 

404. 

1535- 

L.  F. 

— 

4.4^ 

9- 

23. 

1 12. 

433.* 

P. 

2 

4.4 

1 1. 

33- 

185. 

629. 

K. 

2 

3.8 

7.2 

15- 

51- 

86. 

Av.  estimate  of 

stimulus, 

2 

4.2 

10. 

32. 

188. 

750.* 

The  relations  here  expressed  are  graphically  represented 
in  the  accompanying  curves.  The  ordinates  express  the 
estimates  of  the  intensity  of  the  stimulus,  and  the  abscissae 
the  true  intensities  in  grams. 

In  interpreting  these  results  we  may  assume  that  the 
intensity  of  sensation  increases  in  proportion  to  the  esti- 
mated increase  of  the  stimulus.  Such  an  assumption  would 
be  illegitimate,  if  the  stimuli  were  such  that  the  observers 
could  judge  them  by  some  means  other  than  their  effect  on 
sensation.  But  where  the  muscular  sense  is  excluded,  as  in 
these  experiments,  association  cannot  very  well  influence  the 

^  2  g.  was  found  to  be  so  often  inappreciable  by  S.  F.  that  the  determination  based 
upon  it  was  difficult.  The  experiments  on  L.  F.  were  made  before  it  was  decided 
what  weights  had  best  be  used. 

*  These  are  taken  as  units,  as  explained  above. 

'  This  number  refers  to  2500  g.  instead  of  1800  g. 

*  Based  upon  three  values.     See  note  3. 


THE  INTENSITY  OF  STIMULATION. 


23 


results;  for  the  concept  of  weight  is  based  upon  sensations 
of  effort.  Assuming-,  then,  that  a  relation  is  obtained  be- 
tween the  intensity  of  the  stimulus  and  that  of  the  sensation, 

Fig.  3. 


mo   fntensity 


it  is  evident  that  for  moderate  intensities  the  sensation 
increases  much  more  slowly  than  in  direct  proportion  to  the 
stimulus.  As  the  stimulus  approaches  the  pain  threshold, 
the  sensation  appears  to  increase  at  a  much  greater  rate  than 
before.  The  individual  variations  are  so  great  as  to  render 
impossible  an  analytical  expression  of  the  relation.  Never- 
theless, the  shapes  of  the  different  curves  are  similar.  It  is 
clear,  moreover,  that  a  logarithmic  relation  as  demanded  by 
Fechner's  law  does  not  hold,  even  within  narrow  limits,  for 
any  one  of  the  observers.  If  such  were  the  case,  the  esti- 
mates of  the  stimulus  would  increase  arithmetically,  since 
the  stimulus  increases  geometrically. 

It  is,  however,  possible  that  this  relatively  rapid  increase 
for  high  intensities  is  due  to  processes  of  perception  and 
judgment,  and  not  to  real  differences  in  the  rate  of  increase 
of  the  sensation.  As  stimuli  approach  the  pain  threshold, 
the  consciousness  of  impending  pain  may  cause  us  to  over- 
estimate the  magnitude  of  the  stimulus.  This  might  happen 
in  either  of  two  ways.  In  the  first  place,  since  the  sensation 
of  pain  and  that  of  pressure  are  heterogeneous,  we  might 
suppose  that  the  mind  would  unconsciously  assume  great 


24  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

objective  difiEerences  in  quantity  as  causally  related  to  sub- 
jective differences  in  quality.  Another  possible  explanation 
is  that  the  sensation  of  pain,  tending  to  occupy  the  field  of 
consciousness  to  the  exclusion  of  other  presentations,  is  to 
be  considered  as  essentially  a  sensation  of  great  intensity ; 
from  which  it  follows  that  stimuli  causing  pain,  or  approach- 
ing the  pain  threshold,  are  estimated  as  relatively  of  greater 
intensity  than  those  into  the  perception  of  which  the  element 
of  pain  does  not  enter. 

Sec.  6.  Haptic  Sensations  and  Dermal  Pain. 

We  have  already  found,  in  Chapter  I,  that  the  peculiar 
quality  of  the  tickle  sensation  is  not  logically  ascribable  to 
the  quality  of  the  stimulus.  We  may  state,  therefore,  that 
sensations  differing  in  quality  may  be  caused  by  stimuli  differ- 
ing in  quantity.  It  is  not,  however,  near  the  lower  limit  of 
haptic  stimulation  that  this  qualitative  transition  is  most 
marked.  If  pain  be  considered  a  sensation,  two  disparate 
sensations  are  induced  by  high  as  well  as  low  intensities  of 
dermal  stimuli.  If,  however,  pain  be  considered  but  an 
intensive  form  of  an  element  existing  in  all  sensational  states 
of  consciousness,  such  a  generalization  is  impossible. 

According  to  the  commonly  accepted  view,  the  algedonic* 
tone  of  a  sensation  is  negative,  that  is,  unpleasant,  for  very 
low  intensities,  but  upon  increase  in  the  stimulus  becomes 
positive.  As  the  stimulus  is  further  increased,  a  maximum 
of  the  positive  values  is  reached,  after  which  the  algedonic 
tone  rapidly  decreases.  This  doctrine  has,  undoubtedly^ 
many  theoretic  advantages.  But  it  does  not  seem  to  accord 
with  the  observed  phenomena  of  dermal  sensation.  In  the 
experiments  on  pain  already  described,  the  appearance  of 
pain  was  generally  quite  sudden.  If  the  pain  consciousness 
were  merely  an  intensive  form  of  what  accompanies  all 
dermal  stimulation,  we  should  not  expect  such  sudden  trans- 
itions. Then,  too,  in  the  writer's  experience,  at  least,  there 
is  no  pleasurable  element  whatsoever  in  a  haptic  sensation 
of  moderate  intensity.     It  may  be  said  that  we  prefer  certain 

^  Wundt,  op.  cit.  I,  558 ;  Kiilpe,   Grundriss  der  Psychologie,  256.     See  also  the 
writings  of  Ward,  Sully,  and  Bain. 


THE  INTENSITY  OF  STIMULATION.  2$ 

intensities  to  others.  But  this  is  not  necessarily  due  to  dif- 
ferences in  their  algedonic  tone.  The  very  fact  that  one 
stimulus  may  be  preferred  to  another  when  there  is  no  con- 
scious pleasure  or  pain,  tends  to  show  that  the  phenomenon 
is  due  to  complex  processes  of  association.^  The  pressure 
acting  on  a  small  area  will,  on  this  hypothesis,  be  judged 
unpleasant  because  we  tend  to  think  of  the  pain  that  would 
result  if  the  area  were  much  diminished,  or  the  intensity  of 
the  stimulus  much  increased.  In  like  manner,  a  stimulus  of 
moderate  intensity  is  preferable  to  one  of  very  low  intensity, 
because  for  low  intensities  perception  is  less  distinct,  and  we 
tend,  as  a  rule,  to  prefer  things  that  we  can  understand.  At 
least  such  appears  to  be  the  process  in  judgments  of  low 
dermal  stimuli,  so  far  as  the  writer's  introspection  justifies 
any  a  priori  hypothesis. 

But  there  are  also  positive  as  well  as  negative  reasons  for 
considering  the  phenomena  of  dermal  pain  to  be  most  readily 
intelligible  on  the  hypothesis  which  regards  pain  as  a  distinct 
sensation  rather  than  as  a  quale  or  a  psychic  element  of  all 
states  of  consciousness.  In  the  first  place,  pain  has  a 
peculiar  quality  of  its  own,  and  may  occur  unaccompanied 
by  any  other  sensory  element.  When  induced  by  haptic 
stimulation  the  consciousness  of  pain  in  the  part  stimulated 
may  continue  some  time  after  the  removal  of  the  stimulus.^ 

But  there  are  other  points  of  difference  in  the  time  phe- 
nomena of  pain  and  dermal  sensations.  If  we  touch  a  hot 
object  the  sensation  of  contact  precedes  that  of  pain.^  Leh- 
mann  explains  this  by  the  difference  in  the  reaction-times  for 
sensations  of  touch  and  temperature.*  The  same  phenomena, 
however,  occur  when  the  pain  producing  stimulus  is  not 
heat  but  pressure.^  If  a  needle  be  suddenly  pressed  into  the 
skin  a  secondary  pain  will  appear  after  the  sensation  of  pres- 
sure.    In  our  experiments  on  the  pain  threshold  for  impact 

^  Cf.  Dessoir,  op.  cit.,  i86. 
''See  Chap.  VII,  Sec.  2. 
'  Cf.  Dessoir,  op.  cit.,  201,  324. 

*Lehmann,  Die  Hatiptgesetze  des  niensch.  Gefiihlsleben,  44,  45. 
^  Cf.  Goldscheider,  Physiol.  Gesell.,  Oct.,  1890;  Die  Lehre  der  Specif.  Energien 
der  Sinnesorgane,  1881. 


26  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

stimuli  the  same  time  relation  was  observed.^  Marshall 
argues  that  the  pain  consciousness  appearing  under  these 
conditions  is  not  necessarily  a  new  sensation,  but  a  sensa- 
tion X  in  a  painful  phase. ^  But  is  this  not  to  reduce  a 
known  state  of  consciousness  to  one  that  is  unknown  and 
only  assumed?  The  same  criticism,  we  will  remark,  may  be 
made  of  the  explanation  generally  given  of  pains  arising 
from  pathological  processes  in  the  internal  organs  and  in  the 
muscular  and  nervous  tissues. 

Apart  from  introspective  and  experimental  evidence,  the 
sensation  theory  of  pain  is  strongly  corroborated  by  dermal 
pathology.  It  has  been  known  for  many  years  that  tactile 
anaesthesia  may  exist  without  analgesia,  and  analgesia  with- 
out anaesthesia;^  and,  although  hyperalgesia  ma}^  be  so  acute 
that  the  slighest  mechanical  jar  causes  pain,  true  tactile 
hyperaesthesia  is  unknown.* 

The  different  facts  we  have  noted  above  certainly  go  to 
show  that  pain  and  haptic  sensations  are  utterly  disparate 
states  of  consciousness,  and  that  in  all  probability  there  is  a 
corresponding  difference  between  the  physiological  pro- 
cesses. In  fact,  from  the  time  when  Schiff  made  his  cele- 
brated experiments  many  physiologists  have  believed  that 
impulses  for  pain  and  touch  pass  to  the  brain  by  different 
paths.  Goldscheider  claims  even  to  have  discovered  special 
nerves  for  pain ;  but  his  results  have  been  questioned.* 
Wundt  explains  the  physiological  and  pathological  experi- 
ments by  the  altered  excitability  of  the  sensory  nerves  after 
passing  through  the  gray  matter  of  the  cord.^  It  is  possible 
that  at  least  a  partial  cause  of  the  delay  in  the  appearance  of 
pain  is  the  development  of  pathological  processes  in  the  der- 
mal tissues  incited  by  intense  stimulation.  That  the  process 
of  dermal  pain  stimulation  is  somewhat  of  this  nature  is  made 

^  See  Chap.  V,  Sec.  2. 

'Marshall,  op.  cit.,  i8. 

'Wundt,  op.  cit.,  I,  iii ;  Funke,  op.  cit.,  297.  Other  references  are  given  by  these 
writers. 

*Richet,  op.  cit.,  219. 

*  Goldscheider,  Arckiv  fiir  Anat.  und  Physiol.,  1885,  Supp.  Bd.,  87.  For  criti" 
cism  of  G. ,  cf.  Lehmann,  op.  cit.  ;  also  Dessoir,  op.  cit. 

^  Wundt,  op.  cit.,  I,  no,  437,  596;  Funke,  op.  cit.,  297. 


THE  INTENSITY  OF  STIMULATION.  2/ 

probable  by  an  observation  of  Goldscheider.  According  to 
this  writer  the  delay  in  the  appearance  of  pain  upon  stimu- 
lation of  the  foot  of  a  person  afflicted  with  some  disturbance 
of  the  circulation  in  that  part  decreased  appreciably  as  the 
diseased  tissues  were  recovering  to  their  normal  condition.^ 
That  the  delay  is  due,  at  least  in  part,  to  peripheral  pro- 
cesses is  also  borne  out  by  our  own  observations.  In  the 
course  of  experiments  on  the  pain  threshold  for  impact 
stimuli,  the  writer  has  observed  pain  in  the  part  stimulated 
nearly  an  hour  after  the  completion  of  the  experiments. 
And  again,  when  pain  was  induced  only  after  long  continued 
pressure,  it  would  continue  several  seconds  after  the  removal 
of  the  stimulus.^  But  whatever  physiological  hypothesis  be 
accepted,  there  seems  no  doubt  that  there  is  a  qualitative 
physical  difference  in  function  corresponding  to  the  qualita- 
tive psychical  difference  in  sensation. 

Sec.  7.    The  Quality  and  Intensity  of  Sensation. 

In  the  above  discussion  we  have  used  the  terms  quality 
and  intensity  as  applied  to  sensation.  These  terms  have 
been  almost  universally  used  to  denote  fundamental  attri- 
butes of  sensation.^  They  are,  however,  seldom  defined. 
The  term  intensity  is  generally  used  in  the  sense  of  that 
property  of  sensation  which  is  functionally  related  to  the 
intensity  of  the  stimulus.  If,  as  some  have  been  led  to 
believe,  states  of  consciousness  cannot  be  treated  quantita- 
tively, the  term  as  applied  to  sensation  clearly  cannot  be 
used  in  such  a  sense.  Such  a  use  is,  however,  implied  in 
the  word,  since  it  carries  with  it  the  idea  of  physical  quan- 
tity measurable  in  terms  of  space,  to  which  all  physical 
measurements  are  reducible.  But  if  we  reject  the  term 
altogether,  applying  only  the  predicate  qualitative  to  sensa- 
tional changes,  in  what  way  shall  we  describe  subjective 
changes  that  are  discontinuous,  as  opposed  to  those  which 
are  continuous?  On  the  other  hand,  it  may  be  said  that,  if 
the  term  quality  be  thus  restricted,  we  shall  have  no  means 

*  Goldscheider,  Deutsch.  Med.   Wochenschrift,  1890,  no  31. 
»  See  Chap.  VII,  Sec.  2. 

•  Cf.  Wundt,  op.  cit.,  I,  332 ;  Ladd,  op.  cit.,  356 ;  Stumpf,  Tonpsychologie,  I,  350. 


28  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

of  distinguishing  continuous  sensational  changes  due  to 
intensive  variations  from  those  due  to  non-intensive  varia- 
tions in  the  stimulus.  But  we  do  not  think  that  there  is 
necessarily  such  a  difference  in  these  modes  of  subjective 
change.  The  difference  may  be  rather  one  of  perception. 
The  sensational  change  as  haptic  stimuli  are  altered  in  area,  or 
as  auditory  stimuli  are  altered  in  pitch,  is  as  much  a  contin- 
uous, and,  we  think,  quantitative,  change  as  is  that  caused 
by  intensive  variations  in  haptic  and  auditory  stimuli* 
We  are,  perhaps,  accustomed  to  think  of  intensive  sensa- 
tional differences  as  being  measurable,  rather  than  non-inten- 
sive differences,  simply  because  it  is  a  matter  of  familiar 
experience  that  the  corresponding  changes  in  the  stimulus 
are  quantitative  changes,  and  we  are  accustomed  to  estimate 
the  magnitude  of  the  stimulus  by  the  changes  in  sensation. 
If  this  view  be  correct,  we  have  no  term  to  apply  univer- 
sally to  those  changes  in  sensation  that  are  continuous,  as 
opposed  to  those  that  are  discontinuous.  For  from  the 
use  of  the  term  intensity  in  physical  science  it  would  be 
difficult  to  extend  its  meaning  so  as  to  cover  those  changes 
in  sensation  that  are  independent  of  the  intensity  of  the 
stimulus. 


CHAPTER    III. 

The  Discrimination  of  Weights  Without  Effort  and 
THE  Intensity  of  the  Stimulus. 

Sec.  I.  Preceding  Investigations. 

The  comparative  ease  with  which  the  intensity  of  haptic 
stimuli  can  be  measured  renders  the  relation  between  the 
accuracy  of  discrimination  and  the  intensity  of  the  stimulus 
an  attractive  field  for  investigation.  In  fact,  it  was  upon 
experiments  with  weights  that  E.  H.  Weber  based  his  famous 
generalization.  These  experiments  were,  however,  too  few 
and  inaccurate  to  base  a  quantitative  conclusion  upon  them. 
By  simultaneous  pressure  stimulations  Weber  found  the 
least  noticeable  difference  for  32  oz.  to  be  15  oz.  and  10  oz., 
or  about  ^  and  ^  of  the  stimulus,  for  the  two  observers. 
For  32  dr.  the  least  noticeable  difference  for  the  same  observ- 
ers was  found  to  be  8  dr.  and  10  dr.  or  about  |-  of  the  stimu- 
lus. When  the  stimuli  were  applied  in  succession,  the  least 
noticeable  difference  was  found  to  be  -^  to  J^  of  the  stimulus, 
but  Weber  does  not  say  what  intensities  were  used.' 

The  next  research  of  importance  is  that  of  Dohrn,  who 
applied  the  method  of  least  noticeable  difference  to  the 
investigation  of  the  discrimination  of  weights  of  low  inten- 
sities.^ Dohrn  found  that  for  the  volar  surface  of  the  right 
hand  a  weight  of  i  g.  had  to  be  doubled  in  order  for  a  dif- 
ference to  be  perceived.  These  experiments  were  made  on 
himself,  and  also  on  a  boy  of  eleven,  and  must,  therefore,  be 
considered  as  of  little  quantitative  value. 

A  series  of  experiments  with   impact  stimuli  conducted 
by  Biedermann    and    Lowit    is   described    by    Hering,   who 

^  An  account  of  these  experiments  in  more  detail  is  found  in  G.  E.  Muller,  Grund- 
legung  der  Fsycko-physik,  189.     Weber's  original  work  is  inaccessible  to  the  writer. 
*  Dohrn,  Zeitschrift  fur  Rat.  Med.,  3*^  R.,  X,  339. 

29 


30  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

States  that  they  do  not  conform  to  Weber's  law.^  The 
method  of  least  noticeable  difference  was  used,  and  this  is 
sufihcient  to  discredit  the  results,  not  to  speak  of  the  absence 
of  information  as  to  the  other  details  of  the  experiment. 
In  experiments  on  lifted  weights  by  the  same  experimenters, 
the  least  noticeable  difference  for  450  g.  is  stated  to  be  |-  g., 
whereas  for  500  g.  it  is  given  as  -^-^  of  the  stimulus,  a  result 
that  throws  suspicion  on  the  accuracy  of  these  as  well  as  the 
other  experiments. 

The  most  S3^stematic  investigation  of  the  subject  is  that 
of  Merkel,  who  found  the  least  noticeable  difference  at  50  g. 
to  be  y^  of  the  stimulus,  and  to  be  fairly  constant  up  to 
2000  g.^  In  these  experiments  the  pressure  was  exerted 
upon  the  finger  b}^  the  arm  of  a  balance  constructed  for  the 
purpose.  The  muscular  reaction  of  the  finger  may,  there- 
fore, have  affected  the  judgment.  That  this  was  the  case  is 
extremely  probable,  since  Merkel's  results  closely  corre- 
spond with  those  of  the  most  accurate  researches  on  lifted 
weights.^  Then,  too,  Merkel's  experiments  were  made  on 
himself,  and,  as  in  all  such  experiments,  the  knowledge  of 
the  objective  relations  of  the  weights  could  not  but  have 
influenced  the  observer. 

In  an  interesting  series  of  experiments  by  Hall  and 
Motora,  the  least  noticeable  difference  was  found  for  from 
5  g.  to  200  g.  by  changing  the  pressure  at  the  rate  of  y^  of 
the  stimulus  per  second.*  From  5  g.  to  30  g.  this  quantity 
was  about  \  the  stimulus,  after  which  it  increased  consider- 
ably. In  these  experiments  the  time  relations  were  such 
that  the  results  could  not  be  compared  with  those  based  on 
experiments  in  which  successive  stimulation  is  applied.  The 
fact  that  the  intensity  of  pressure  sensations  decreases  rap- 
idly, at  least  for  low  intensities,  after  the  application  of  the 
weight,  makes  the  problem  one  of  considerable  perplexity.^ 

We  know  of  no  other  work  on  the  subject  to  the  record 

^  Hering,  Sitzungsber.  der  Wiener  Acad.,  3*^  Abth.,  LXXII,  342,  as  given  in 
Miiller,  op.  cit.,  200. 

*  Merkel,  Philosophische  Studien,  V,  253. 

^  Cf.  Fullerton  and  Cattail,  op.  cit.,  122;  Merkel,  op.  cit.,  261. 

*  Hall  and  Motora,  Amer.  Journ.  of  Psy.,  I,  72. 

*  See  Chapter  VII,  Sec.  i. 


THE  DISCRIMINATION  OF  WEIGHTS   WITHOUT  EFFORT.     3 1 

of  which  we  have  access,^  except  that  of  Pierce  and  Jastrow.* 
In  this  research  the  probable  error  for  250  g.  was  found  to 
be  -^-^  of  the  stimulus,  and  to  be  further  decreased  by  prac- 
tice. The  relation  of  the  probable  error  to  the  magnitude 
of  the  stimulus  was  not  considered.  In  these  experiments 
the  pressure  was  exerted  through  the  muscles,  and  therefore 
it  is  probable  that,  as  in  Merkel's  experiments,  the  discrimi- 
nation for  effort  is  what  is  measured. 

Sec.  2.   Further  Experiments :     Method  of  Procedure. 

There  being  no  satisfactory  determination  of  the  accuracy 
of  discrimination  for  objective,  as  opposed  to  subjective 
pressure,  a  series  of  experiments  was  made  in  the  following 
way.  The  left  hand  of  the  observer  was  placed  on  the  table, 
comfortably  supported,  and  in  such  a  manner  that  the  palm, 
which  was  turned  upward,  was  fairly  level.  The  eyes  of  the 
observer  being  closed,  two  weights  were  placed  successively 
upon  the  hand,  and  the  observer  was  required  to  judge  which 
was  heavier  by  the  method  of  right  and  wrong  cases.  When 
no  difference  was  perceived  the  observer  was  required  to 
guess.  The  stimuli  with  the  smaller  areas  were  placed  on 
different  parts  of  the  region  covered  by  the  large  area.  The 
place  was  constant,  however,  for  every  two  compared.  The 
degree  of  confidence  was  recorded  by  having  the  observer 
use  four  letters,  a,  b,  c  and  d,  according  to  his  confidence. 
The  apparatus  used  is  shown  in  the  accompanying  cut. 

The  weights  used  were  cylindrical  boxes,  B,  filled  with 
shot,  the  sides  being  built  up  when  necessary  by  stiff  paper. 
To  the  bottom  of  the  box  was  affixed  a  projecting  piece  of 
the  shape  of  a  fustrum  of  a  cone,  N,  the  base  of  which  came 
in  contact  with  the  skin.  In  this  way  a  small  area  of  stimu- 
lation could  be  obtained.  The  material  in  contact  with  the 
skin  was  thick  cardboard,  so  that  the  influence  of  tempera- 
ture was  practically  excluded.  Projecting  upward  from  the 
centre  of  the  box  was  an  iron  rod,  AC,  which,  on  being 
inserted  within  the  glass  support,  M,  of  a  chemist's  stand,  S,. 

^  We  have  not  access  to  the  dissertation  of  Bastelberger,  Exper.  Prilf.  der  zu 
Drucksinn  angewandten  Metkoden,  Stuttgart,  1879. 

'  Pierce  and  Jastrow,  National  Academy  of  Sciences,  1884,  III,  75. 


32 


SENS  A  TIONS  FROM  PRESSURE  AND  IMPACT. 


prevented  the  weight  from  tipping  over,  as  it  would  other- 
wise have  done  when  the  smaller  area  of  stimulation  was 
used.  The  weights  were,  of  course,  always  placed  so  as  to 
be  as  nearly  as  possible  perpendicular  to  the  hand.  In  order 
to  obviate  slight  differences  in  the  surface  applied,  the  same 


K 


M 


i 


B 


nV 


Fig.  4. 


box  was  used  to  give  the  variable  and  the  standard  stimulus. 
The  increment  of  weight  consisted  of  a  bag  of  shot  which 
could  be  placed  in  the  box  without  being  noticed  by  the 
observer.  The  stimuli  applied  were  as  described  above, 
except  that  having  a  weight  of  3200  g.  This  consisted  of 
three  cylindrical  kilogram  weights  placed  one  over  the  other. 
Through  these  weights  ran  an  iron  rod,  which  served  as  a 
support  as  with  the  other  weights.  To  the  base  was  affixed 
a  small  box  loaded  with  shot,  so  as  to  make  a  total  weight  of 
3200  g.  The  base  consisted  of  circular  cardboard.  The 
time  relations  were  fairly  constant.  The  careful  application 
and  removal  of  the  weights  by  the  experimenter  made  it  im- 
possible to  have  the  times  of  application  and  the  intervals 
between  the  stimulations  as  constant  as  might  be  desired. 
It  was  found,  however,  by  having  the  observer  note  these 
times,  that  they  did  not  vary  appreciably  from  2  sec.  and 
3  sec.  respectively.  Moreover,  the  judgment  of  weight 
seems  to  be  easiest  as  soon  as  the  hand  receives  the  full 
force  of  the  weight,  and  the  accuracy  of  discrimination  does 
not  vary  appreciably  when  the  interval  between  the  applica- 


THE  DISCRIMINATION  OF  WEIGHTS  WITHOUT  EFFORT.     33 

tion  of  the  two  stimuli  is  not  greater  than  lo  sec.^  No  fixed 
order  was  used  in  applying  the  stimuli,  the  only  require- 
ment being  that  for  a  series  of  lOO  experiments  in  50  the 
second  weight  should  be  heavier,  and  in  the  other  50  lighter. 
About  10  sec.  intervened  between  two  successive  experiments, 
but  no  effort  was  made  to  have  this  constant.  At  one  sit- 
ting 20  or  25  experiments  in  a  given  series  were  made.  Then 
the  observer  rested  a  few  minutes,  and  another  set  of  experi- 
ments was  made.  The  time  devoted  to  the  experiments  at 
one  sitting  varied  generally  from  an  hour  to  an  hour  and  a 
half.  In  order  that  the  influence  of  fatigue  might  be  the 
same  for  the  different  intensities  used,  the  order  in  which 
the  different  sets  of  experiments  for  the  different  series  was 
made  was  varied,  so  that  a  given  intensity  would  be  used  as 
much  in  the  first  as  in  the  latter  part  of  the  sittings.  The 
observers  were  students  of  Psychology,  with  some  previous 
practice  in  experimental  work.^  The  experiments  were  be- 
gun in  March,  1892,  and  completed  in  June,  1893. 

With  regard  to  possible  sources  of  error,  most  of  them, 
we  think,  were  eliminated.  In  applying  the  weights  with 
the  hand,  it  is  impossible  to  control  properly  the  velocity  of 
impact.  The  writer  endeavored  to  obviate  this  difficulty  by 
applying  the  weights  slowly  and  carefully.  In  this  way  the 
error  may  be  neglected  for  weights  of  sufificient  intensity  to 
cause  a  distinct  sensation  of  pressure  apart  from  one  of 
impact.  For  weights  of  100  g.  and  200  g.,  however,  the 
depression  of  the  skin  due  to  the  pressure  is  so  slight  that 
impact  cannot  be  entirely  neglected.  The  rate  of  applica- 
tion was,  however,  kept  as  constant  as  practicable.  Then, 
as  is  shown  in  Chapter  V,,  the  discrimination  of  weights  by 
impact  is  about  the  same  as  by  pressure.^ 

Another  source  of  error  lies  in  the  slight  variations  of 
the  weight  from  a  perpendicular  position  and  consequent 
pressure  upon  the  glass  support.     For  the  purpose  of  inves- 

'  Cf.  W^eber,  op.  cit.,  545,  where  it  is  stated  that  there  is  no  appreciable  differ- 
ence in  the  accuracy  of  discrimination  after  an  interval  of  30  sec.  A  far  more  accurate 
investigation  of  the  matter  is  that  of  Fullerton  and  Cattell,  op.  cit.,  148. 

''■  The  writer  would  take  this  occasion  to  express  his  appreciation  of  the  kindness 
of  those  who  have  devoted  so  much  time  to  these  and  other  experiments,  and  to  ex- 
press his  gratitude  for  the  assistance  so  generously  given. 

^SeeCh.  V.,  Sec.  4. 


34  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

tigating  this  source  of  error,  a  formula  was  deduced  for  the 
decrease  in  the  amount  of  pressure  exerted  upon  the  hand 
when  the  weight  was  not  perpendicular.  If  C  be  the  centre 
of  gravity  of  the  mass,  D  the  point  of  application,  the  area 
being,  for  convenience,  considered  inappreciable,  A  the 
point  of  application  of  the  rod  upon  the  glass  support,  W 
the  weight,  and  S  the  angular  deviation  from  the  perpen- 
dicular of  the  line  through  C,  D  and  A ;  then  for  the  loss  of 
weight  at  D,  which  we  shall  call  x,  we  shall  have, 

X  =  Wsin^  <^ -^-yy 

In  this  formula  it  is  assumed  that  at  the  point  A  there  is 
such  friction  that  the  mass  is  not  free  to  move.  By  observ- 
ing what  appeared  to  be  approximately  the  maximum  value 
of  ^  in  the  experiments,  the  corresponding  value  of  x  for  a 
weight  of  500  g.  was  found  by  the  formula  to  be  1.2  g.  An 
experimental  determination  of  this  quality  was  also  made 
by  means  of  the  balance.  A  500  g.  box  with  sharpened  base 
was  placed  in  the  pan,  so  that  the  rod  in  contact  with  the 
glass  support  deviated  from  the  perpendicular  to  about  the 
same  extent  as  that  which  was  found  to  be  the  maximum  de- 
viation in  the  experiments.  The  loss  of  weight  was  found  to 
be  1.5  g.  Inasmuch  as  the  measurement  was  rendered  inex- 
act by  the  horizontal  component  of  the  pressure  exerted, 
the  result  corresponded  as  closely  as  was  expected  with  that 
obtained  by  calculation.  The  true  loss  of  weight  was,  how- 
ever, much  less  than  this  for  the  stimuli  used ;  for  the  place 
of  application  having  considerable  area,  it  is  evident  that  the 
weight  will  tend  to  be  in  more  stable  equilibrium.  Then 
the  true  error  is  not  the  average  loss  of  weight,  but  the 
variation  from  this  average,  which  is  of  course  much  less. 
We  may,  therefore,  neglect  this  source  of  error  entirely. 

In  every  set  of  100  experiments,  in  50  of  which  the 
second  weight  was  lighter  and  in  50  heavier,  the  percent- 
age of  right  answers  was  calculated  for  both  groups  of  50 
answers.  The  accuracy  of  discrimination,  h,  was  deter- 
mined from  these  data  by  tables  based  upon  the  well-known 
formula : 

r  I  /*h  A  =  t 

5=1    +    ^    je-t«dt 
n  V  ir*A 


THE  DISCRIMINATION  OF  WEIGHTS  WITHOUT  EFFORT.     35 

In  the  tables  used*  the  values  of  p        were  given,  instead 

of  those  of  hA,  P.E,  being  the  probable  error,  or  that 
error  which  would  be  equal  to  A,  when  the  percentage  of 
right  cases  is  75.     Tables  giving  the  values  of  h^  may  be 

readily  changed  so  as  to  give  the  values  of  p-^r  by  substi- 
tuting for  h  the  expression  p^  .     In  some  of  the  series  it 

was  found  that  the  constant  error,  or  tendency  to  overesti- 
mate the  second  stimulus,  was  so  great  that  the  use  of  a 
larger  increment  was  necessary  when  the  second  weight  was 
lighter.  For  otherwise  the  second  weight  would  have  been 
judged  heavier  the  great  majority  of  trials ;  and  the  observer, 
therefore,  would  have  acquired  the  habit  of  judging  the 
second  weight  the  heavier,  which  would  have  vitiated  the 
experiments.  This  involved  the  use  of  special  formulae, 
which  we  now  give.     C.E.  is  the  constant  error,  P.E.  the 

probable  error,  T,  the  value  in  the  table  for  p  ^    when  the 

second  weight  is  lighter,  T^  the  value  when  it  is  heavier, 
and  Ajj  and  Aj  are  the  increments  used  when  the  second 
weight  is  heavier  or  lighter. 

Case  I. 

When  no  constant  error  occurs,  real  or  apparent,  Aj^  = 
A,  =  A,  and  T^  =  Ti  =  T.     Then 

P.E.        ^' 
whence, 

P.E.  =  ^. 

Case  II. 

When  a  constant  error  occurs,  and  only  one  increment  is 
used,  we  have, 

'  Given  by  Fullerton  and  Cattell,  op.  cit.,  i6.  They  will  also  be  found,  in  different 
form,  in  Philosoph.  Studien,  IX,  145  ;  and  in  Fechner,  Elemente  der  Psychophysik, 
\V^  Auf.,  Leipzig,  1889,  108. 


36  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

A      4-      C.E.  r^  .A     -      C.E.  r^ 

P.E.        =  ^-^""^       P.E.      =  ^- 
whence, 

P.E.  =  T=r4Ar.  and  C.E.  =T,  P.E.  -A 

-•-h  "T    J-i 

Case  III. 
If  a  constant  error  occurs,  and  Aj^is  >  Aj  or  <  A„  we  have, 

P.E.  =  ^  2  T '  ^^^  ^•^-  =  ^^  P-^-  —  ^^- 
Case  IV. 

If  both    stimuli  are   equal   when    the    second   is    judged 
heavier,  i.  e.,  if  Aj,  =  O,  we  have, 

PE  ^ 

and 

C  =  P.E.  Tj. 

Case  V. 

If  the  first  stimulus  is  greater  than  the  second,  when  the 
second  is  judged  heavier,  Aj^  is  minus,  and  we  have, 
-A,  +  C.E.  _ 
P.E.  ~     ^' 

and 


whence, 


and 


J- 
If  the  conditions  are  the  same  as  in  Case  V.,  but  —  <x\'V 

when  the  second  weight  is  judged  lighter,  calling  the  value 

of  the  probability  integral  corresponding  to  lOO ,  T^^,  we 

have 

C.E.  -A,_^ 
P.E.       "~     ^' 


^ 

-  C.E. 
P.E. 

= 

Tn 

P.E.  =  ^ 

,+ 

A. 

C.E. 

=  P.E. 

T. 

+  K 

Case  ' 

V\. 

THE  DISCRIMINATION  OF  WEIGHTS  WITHOUT  EFFORT.     37 

and 


whence, 
and 


C.E.  -A,_ 
P.E.       "~^i' 

PE   ^^1—^ 

C.E.  =  P.E.  T,4-A,. 

Case  VII. 

If  the  conditions  are  the  same  as  in  Case  VI.,  except 
that  no  increment  is  used  when  the  second  weight  is  judged 
heavier,  we  have 


and 


p  -p 


C.E.  -=T^P.E. 


Case  VIII. 


If  the  conditions  are  the  same  as  in  Cases  VI.  and  VII., 
except  that  for  the  second  to  be  judged  heavier,  an  incre- 
ment is  used,  +  A^,  we  have 

P  F    -  ^1-^  ^h 

and 

C.E.  =  P.E.  T, -A,. 

By  the  above  formulae  were  calculated  the  values  of  P.E. 
and  C.E.  for  each  set  of  100  experiments.^  That  under  Case 
II.  was  used  in  the  great  majority  of  the  calculations.  Such 
increments  were  generally  used  as  would  give  a  percentage 
of  right  cases  as  near  as  possible  to  84  per  cent.,  since  fewer 
observations  are  needed  for  such  a  value  of  A  in  order  to 
calculate  the  value  of  P.E. 

The  value  of  P.E.  thus  found  is  not  strictly  that  for  the 
standard  stimulus,  but  is  compounded  of  this  and  its  value 

^  In  order  to  test  the  approximate  accuracy  of  the  formulas,  the  value  for  C.E.  thus 
found  was  added  to  the  second  stimulus,  and  it  was  noted  whether  the  conditions  were 

such  as  to  give  about  the  value  of  —as  expected  from  the  value  calculated  for  P.E. 


38  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

for  the  variable  stimulus.^  When  the  increment  is  very 
small  this  error  may  be  neglected.  But  in  some  of  our  ex- 
periments, on  account  of  the  magnitude  of  the  constant 
error,  an  increment  was  used  of  from  ^  to  ^  of  the  stimulus. 
This  difficulty  cannot  be  overcome  unless  the  relation  of  the 
probable  error  to  the  stimulus  is  known.  Inasmuch  as  we 
found  that  this  relation  was  approximately  that  demanded 
by  Weber's  law,  at  least  within  certain  limits,  we  corrected 
the  values  of  P.E.  on  this  assumption.  The  result  will  at 
least  be  more  correct  than  it  would  if  such  a  correction  were 
not  made,  even  if  the  probable  error  increased  more  slowly 
than  is  assumed.  To  make  such  a  correction,  let  S  be  the 
standard  stimulus,  P.E.  the  probable  error  obtained  from 
the  formulae  above  given,  and  F.E,,^  the  value  of  P.E.  cor- 
rected for  the  standard  stimulus.  Then  P.E.  may  be  con- 
sidered as  approximately  the  arithmetic  mean  of  the  proba- 
ble errors  for  the  stimuli  used.     We  shall  have,  therefore, 


P.E.  =- 
whence, 


P.E.,+ P.E,.  (A  +  A)  +  P.E.,i5l  +  A) 
4 

4S 


^•^•^=P-E-{4ST^TAJ- 


Sec.  3.    Results. 

The  values  of  P.E.  given  in  the  tables  below  are  the  cor- 
rected values.  In  the  majority  of  cases  they  do  not  differ 
appreciably  from  the  uncorrected  values,  but  at  times  the 
difference  is  considerable.  No  correction  was  made  for  the 
constant  error,  since  its  relation  to  the  magnitude  of  the 
stimulus  is  more  complex. 

In  the  appended  tables  the  standard  stimuli  used  are 
given  in  the  first  column.  Then  follow  the  different  proba- 
ble errors  for  each  set  of  100  experiments,^  P^,  Pj,  etc.,  and 
their  averages  and  mean  variations.  The  other  columns 
give  the  different  constant  errors,  C^  Cg,  etc. 

*Cf.  Miiller,  op.  cit..  21 

■  The. probable  errors  for' N.  F.  and  J.  S.  are  based  upon  80  experiments. 


THE  DISCRIMINA  TION  OF  WEIGHTS  WITHO  UT  EFFOR  T.      39 

Observer,  N,  F. ;  area,  8  cm. 


s 

Pi 

P2 

Ps 

P4 

Av. 

M.  V. 

Ci 

C2 

C3 

C4 

Av. 

M.  V. 

200 

31 

21 

16 

21 

22 

4. 

17 

17 

16 

17 

17 

0. 

800 

255 

138 

72 

86 

137 

59 

120 

164 

176 

159 

155 

17 

1600 

191 

221 

185 

175 

193 

18 

157 

143 

280 

200 

195 

43 

3200 

341 

474 

— 

— 

408 

44 

119 

222 

— 

170 

57 

Observer,  J. 

S. ;  area,  8  cm. 

S 

Pi 

Va 

Av. 

M.  V. 

Ci 

C. 

Av. 

M.  V. 

800 

134 

97 

115 

18 

II 

30 

20 

9 

1600 

148 

207 

177 

28 

51 

100 

75 

24 

3200 

244 

261 

252 

8 

149 

121 

135 

14 

Observer,  R. ;  area,  8  cm. 


s 

Pi 

P2 

Ps 

Av. 

M.V. 

Ci 

C. 

C3 

Av. 

M.V. 

100 

25 

27 

19 

23 

3 

17 

16 

37 

23 

9 

500 

102 

121 

83 

102 

13 

70 

120 

166 

119 

32 

1500 

248 

337 

229 

271 

43 

631 

799 

682 

704 

63 

Observer 

Mc 

W.; 

area,  8 

cm. 

S 

Pi 

P2 

Ps 

P4 

Ps 

Av. 

M.V. 

Ci 

Ca 

C3 

C4 

Cs 

Av. 

M.V. 

100 

20 

24 

24 

14 

16 

19 

3 

I 

0 

15 

5 

2 

4 

4 

500 

2,2> 

42 

31 

40 

33 

36 

4 

-13 

-13 

2 

-24 

2 

-9 

9 

1500 

no 

130 

no 

100 

109 

112 

7 

6 

9 

6 

18 

12 

10 

4 

3200 

233 

183 

156 

196 

197 

193 

19 

96 

286 

200 

233 

285 

218 

56 

40  SENS  A  TIONS  FROM  PRESSURE  AND  IMPACT. 

Observer,  L.  S. ;  area,  8  cm. 


s 

Pi 

P2 

P3 

P4 

Ps 

Av. 

M 

.  V. 

Ci 

C2 

C3 

C4 

Cs 

Av. 

M.V. 

lOO 

17 

20 

17 

19 

16 

18 

I 

-4 

-3 

I 

6 

0 

0 

3 

500 

37 

29 

39 

42 

47 

39 

4 

-12 

—2 

-6 

0 

-II 

-6 

3 

1500 

114 

100 

114 

103 

III 

108 

5 

0 

67 

13 

57 

69 

41 

28 

3200 

243 

217 

256 

206 

243 

233 

17 

85 

195 

125 

70 

239 

143 

59 

Observer,  L.  S. ;  area,  -^^  cm. 


s 

Pi 

P2 

P3 

P4 

P5 

Av. 

M.V. 

Ci 

C2 

C3 

C4 

Cs  Av. 

M.V. 

100 

9 

14 

13 

16 

16 

13 

2 

I 

—I 

I 

I 

4 

I 

I 

500 

43 

29 

35 

57 

41 

41 

7 

0 

—2 

-14 

17 

19 

4 

8 

1500 

124 

91 

127 

105 

105 

no 

II 

59 

49 

III 

74 

74 

73 

15 

Observer,  N.  F. ;  area,  -^-^  cm 


s 

Pi 

P2 

P3 

P4 

Av. 

M.V. 

Ci 

C2 

C3 

C4 

Av. 

M.V. 

200 

36 

77 

— 

— 

56 

20 

48 

30 





39 

9 

800 

87 

121 

120 

125 

113 

12 

195 

146 

65 

70 

119 

51 

1600 

227 

231 

196 

158 

203 

26 

259 

263 

215 

^ZZ 

217 

44 

Observer,  J.  S.  ;  area,  -f-^  cm 


s 

Pi 

P2 

Av. 

M.V. 

Ci 

C2 

Av. 

M.V. 

800 

1600 

104 
221 

103 
171 

103 
196 

0 
25 

-26 

94 

-26 
0 

-26 
47 

0 
47 

THE  DISCRIMINA  TION  OF  WEIGH  TS  WI THO  U  T  EFFOR  T.      4 1 


These  results  are  graphically  represented  in  the  accom- 
panying curves. 


Prob. 

jpr. 

Error 

y^ 

R        ^ 

J.S.. 

Fig.   5 — Large  Area. 


Prob. 
error. 


Stinu 


Fig.  6 — Small  Area. 


In  the  above  experiments  no  stimuli  were  used  less  than 
100  g.  Less  extended  experiments  were  made  on  S.  F.,  an 
excellent  observer,  for  a  standard  stimulus  of  5  g.,  the  varia- 
ble stimulus  being  7  g.  The  stimuli  used  were  cylindrical 
pieces  of  lead.  To  the  bottom  was  fastened  a  circular  piece 
of  cardboard,  having  a  diameter  of  1.5  cm.  The  weights 
were  carefully  lowered  upon  the  palm  of  the  hand  by  iron 
rings  projecting  from  the  tops.  Below  are  the  values  of  the 
three  probable  errors  obtained  for  each  set  of  100  experi- 
ments, and  also  the  value  of  the  average  divided  by  the 
mean  of  the  stimuli  used. 


Observer,  S.  F. 
Stimulus.         Fy 
5  g-  and  7g.      3.7 


I.: 


^  3 
2.0 


Av.  P. 

2.5 


S 
P 

•4 


42  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

These  results  may  be  taken  as  representative  for  good 
observers,  since  the  probable  error  for  S.  F.  at  looo  g.,  and 
with  the  same  area,  was  found  by  200  experiments  to  be 
about  -^  of  the  stimulus,  which  is  fairly  typical. 

It  is  evident  from  the  above  results  that  Weber's  law 
holds  fairly  well  between  the  approximate  limits,  300  g.  and 
3000  g.  For  very  low  stimuli  the  probable  error  increases 
much  more  slowly  than  the  stimulus.  For  high  intensities 
it  increases  somewhat  more  slowly,  though  the  deviation  is 
not  very  marked.  It  is  probable  that  observers  differ  some- 
what not  only  in  their  absolute  accuracy  of  discrimination, 
but  even  in  the  relation  of  this  accuracy  to  the  magnitude  of 
the  stimulus.  This  is  shown  in  the  curves  for  L.  S.,  J.  S., 
and  McW.  (Figure  2),  that  of  J.  S.  clearly  departing  from 
the  straight  line  demanded  by  Weber's  law.  The  irregular 
shape  of  N.  F.'s  curve  is  perhaps  to  be  explained  by  the 
decided  variation  in  his  accuracy  of  discrimination,  as  shown 
in  the  tables.  If  it  be  assumed  that  such  variation  is  the 
cause  of  the  irregularity  of  the  curve,  it  is  evident  that  for 
this  observer  the  probable  error  increases  in  direct  propor- 
tion to  the  stimulus  within  the  limits  used. 

Summarizing  the  quantitative  results  obtained,  the  maxi- 

P  E 

mum  value  of  — ^'  for  a  set  of   100  experiments  was  \,^  the 

minimum  ^,^  and  the  average  for  all  observers  and  all  inten- 
sities above  100  g.  was  \. 

It  is  evident  that  individuals  of  about  the  same  age  and 
social  class  differ  somewhat  in  their  discrimination.  Of  the 
eight  observers  tested  only  two  showed  much  variation  from 
the  average,  N.  F.  and  R.  having  as  their  relative  probable 
errors  \  and  \.  From  both  of  these  observers  the  writer 
would  have  expected  at  least  as  good  results  as  from  others. 
Both  complained  of  a  tendency  to  drowsiness  in  the  course 
of  the  experiments,  and  to  this  their  low  accuracy  may  per- 
haps be  ascribed. 

^  Calculations  based  upon  only  lOO  experiments  are,  of  course,  somewhat  affected 
by  the  variable  error. 


THE  DISCRIMINA  TION  OF  WEIGHTS  WITHO  UT  EFFOR  T.      43 

Sec.  4.    The  Constant  Error. 

It  has  for  many  years  been  known  that  in  comparing  two 
stimuli  applied  successively,  there  is  in  general  a  tendency 
to  overestimate  the  second.  In  no  instance  known  to  the 
writer  has  a  constant  error  of  such  magnitude  been  observed 
as  those  shown  in  the  records  of  R.  and  N.  F.,  which  were 
for  some  stimuli  as  great  as  \  of  the  stimulus.  The  value  of 
C  E.  seems  to  increase  with  the  stimulus,  but  not  in  direct 
proportion.  It  is  very  small  or  even  negative  for  low  inten- 
sities, but  increases  rapidly,  apparently  soon  reaching  a  maxi- 
mum. Some  persons  do  not  show  any  constant  error  except 
for  very  high  intensities.  Experiments  on  L.  F.  showed  no 
constant  error  for  1000  g.,*  but  at  3200  g.  it  was  appreciable. 

Persons  having  a  large  constant  error  tend  to  have  a  large 
probable   error.     This  is  shown  by   the  following  average 

P  E  C  E 

values,  in  round  numbers,  of     '(^     and  — ^— ^  for  8  persons. 

L.  F.^     S.  F.'     McW.     L.  S.     J.  S.     W."     N.  F.     R. 


^    iV 

iV 

tV 

1 

i 

1 

T 

1 

A   C.E. 
Av.   . 

[zero]  [zero] 

A 

1 

1 
■S7 

^ 

^ 

1 

Whether  the  constant  error  influences  the  probable  error 
or  vice  versa,  we  cannot  say.  Possibly  these  magnitudes  are 
causally  related  to  some  process  affecting  them  both. 

The  constant  error  appears  to  vary  more  than  the  proba- 
ble error.  Below  are  given  the  relative  mean  variations  of 
the  probable  and  constant  error.  They  are  calculated  by 
taking  the  mean  of  the  values  of  the  mean  variation  divided 
by  the  probable  or  constant  error,  as  the  case  may  be.  We 
_give  also,  for  the  sake  of  comparison,  the  average  value  of 
P.E. 


S 


for  the  different  observers. 


^  See  Chapter  V,  Sec.  5. 

*  The  experiments  on  W.,  L.  F.  and  S.  F.  will  be  given  in  Chap.  V.,  Sec.  4,  and 
Chap.  VI.,  Sec.  5.  The  standard  stimulus  was  not  varied,  being  200  g.  for  W.  and 
1000  g.  for  L.  F.  and  S.  F. 


44  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

N.F.       J.S.       R.       L.S.        McW.       W. 
M.V. 


P.E. 
M.V. 

C.E. 
P.E. 

1 

3" 

1 
TIT 

1 

1^ 

1 
To 

2 

* 

i 

i 

1 

3 
■5" 

2 
■5" 

\ 

1 

i 

1 

TIT 

tV 

1 

s 

Since  there  is  in  general  greater  variation  in  C.E.  than 
in  P.E.,  we  conclude  that  these  variations  are  to  some 
extent  true  variations  rather  than  chance  variations  due  to 
the  conditions  of  the  experiment.  The  variation  of  the  con- 
stant error  was  most  noticeable  in  the  case  of  an  observer, 
E.  G.,  on  whom  in  two  weeks  over  500  experiments  were 
made.  In  these  experiments  the  value  of  C.E.  increased  so- 
rapidly  that  no  calculations  could  be  made.  At  first  it  was 
inappreciable  for  100  g.,  500  g.  and  i5oog.  ;  but  it  increased 
with  practice  until  for  100  g.  it  was  apparently  as  great  as 
the  stimulus,  and  for  the  higher  intensities  from  1  to  I-  as 
great.  The  theoretical  importance  of  these  variations  lies 
in  the  application  of  the  probability  integral  to  the  method 
of  right  and  wrong  cases,  for  in  this  integral  P.E.  and  C.E. 
are  assumed  to  be  constant. 

If  the  constant  error  be  due  to  central  processes,  we 
should  expect  individuals  having  a  great  error  for  pressure 
to  have  a  similarly  great  error  for  lifted  weights.  But  this 
is  not  the  case.  R.,  who  had  the  greatest  C.E.  of  all  the 
observers,  failed  to  show  the  slightest  trace  of  any  overesti- 
mation  in  forty  experiments  with  lifted  weights.  L.  S.  and 
McW.  likewise  had  no  appreciable  C.E.  for  lifted  weights  of 
high  intensity,  though  they  had  for  pressure  stimuli  of  high 
intensity.  Not  only  this,  but  a  constant  error  for  pressure 
does  not  apparently  involve  one  for  impact.  At  least  in  25 
experiments  on  R.,  no  C.E.  was  appreciable  for  50  g.  falling 
20  cm. 

Sec.  5.    The  Confidence  of  the  Observer. 

The  confidence  of  an  observer  in  estimating  stimuli  not 
differing  greatly,  varies  from  complete  doubt  to  complete 
certainty.     The  degree  of  confidence  depends  upon  the  mag-^ 


c. 

d. 

37  per  cent. 

5  per  cent 

55 

12    " 

THE  DISCRIMINA  TION  OF  WEIGH  TS  IV I THO  U  T  EFFOR  T.       45 

nitude   of  the   difference   of    the   stimuli,    and  consequently 
upon  the  probability  of  correctness.^ 

In  the  experiments  on  the  discrimination  of  weights,  ob- 
servers were  requested  to  say  a  when  certain,  b  when  fairly 
confident,  c  when  less  confident  and  almost  doubtful,  and  d 
when  unable  to  decide  except  by  guessing.  The  results  for 
different  observers  are  now  given.  The  figures  indicate  the 
percentages  of  times  the  different  letters  were  used  when 
the  observer  was  right  and  also  when  he  was  wrong. 

McW. 

a.  b. 

r.     14  per  cent.  44  per  cent, 
w.     4   "      29   '' 

L.  S. 

r.      I  per  cent.   17  per  cent.  73  per  cent.  9  per  cent. 
w.    —  3   "      70   "     27   " 

R. 

r.     —  13  per  cent.  78  per  cent.  9  percent, 

w.    —  6   "      78    "     16   '' 

J.  S. 

r.     —  yj  per  cent.  92  per  cent,   i  per  cent, 

w.    —         22    "      98   "      — 

N.  F. 

r.      2  per  cent.   24  per  cent.  66  per  cent.  18  per  cent. 

w.     8   ''      27   ''      59   ''      6   " 

As  the  percentage  of  right  cases  varied  for  different  ob- 
servers, we  cannot  express  their  degree  of  confidence  by  the 
percentage  of  times  a  and  b  were  used.  We  may,  however, 
use  as  a  rough  indication  of  individual  differences  the  fraction 

— ,  that  is,  the  ratio  of  the  number  of  times  he  was  confident 
w 

when  wrong  to   the  total  number  of  times  he  was  wrong. 

This    fraction    is    for    L.    S.    only   y|-g-;    for    R.,    i^-^',    for 

McW.,  tVit''   for  J-   S.,  tI^;   and  for  N.  F.,  ^-W     By  com- 

*  In  experiments  on  lifted  weights  described  by  Fullerton  and  Cattell,  the  degree 
of  confidence  varies  nearly  as  the  percentage  of  right  cases.     Op.  cit.,  126. 


46  SENS  A  TIONS  FROM  PRESSURE  AND  IMPACT. 

paring-  these  numbers  with  the  relative  probable  errors,^ 
we  see  that  there  is  no  relation  between  the  two  quantities.^ 
As  will  be  seen  from  the  above  results,  the  observers  were 
seldom  certain.  It  is  remarkabl-e,  however,  that  two  ob- 
servers were  certain  4  per  cent,  and  8  per  cent,  of  the  time 
respectively  when  they  were  wrong.  We  might  suppose 
that  the  probability  of  correctness  when  coniident  would  be 
inversely  related  to  the  degree  of  confidence,  as  shown  by 

the  fraction  —  above  mentioned.     This  does  not  appear  to 
w 

be  the  case.     For  McW.   and  J.  S.  the  probability  of   cor- 

rectness  when  confident  was  A^;   but  the  values  of  —  for  the 

two  observers  were  quite  different. 

The  number  of  times  the  observers  were  correct  when 
guessing  was  greater  than  could  be  explained  by  chance. 
By  taking  the  number  of  d' s  in  ten  separate  sets,  of  from 
100  to  150  each,  and  computing  the  percentage  of  right  cases, 
it  was  found  that  in  all  of  these  ten  sets  this  percentage  was 
over  50  per  cent.,  the  average  being  59  per  cent.^  From 
this  it  follows  that  to  halve  the  number  of  doubtful  answers 
and  add  this  to  the  number  of  right  cases,  as  has  generally 
been  done,  is  an  illegitimate  method  of  procedure,  since 
based  on  an  erroneous  assumption.  In  the  case  of  some 
observers  whose  confidence  was  small,  this  percentage  ran 
as  high  as  65  per  cent,  and  70  per  cent.  The  bearing  of  this 
on  the  method  of  least  noticeable  differences  is,  we  think, 
quite  obvious.  F.,  about  70  per  cent,  of  whose  guesses 
were  correct,  stated  explicitly  that  when  guessing  he  felt  no 
difference  whatsoever,  and  that  his  judgment  was  entirely  a 
guess.  But  apart  from  problems  of  method,  such  facts  are 
of  not  a  little  theoretic  importance,  since  they  show  clearly 
the  possible  accuracy  of  unconscious  mental  processes. 

^  See  Sec.  4  of  this  chapter. 

*  Fullerton  and  Cattell  found,  contrary  to  this,  that  observers  having  the  largest 
probable  errors  had  the  greatest  confidence.     Op.  cit.,  126. 

'  This  corresponds  with  the  results  of  Fullerton  and  Cattell  for  lifted  weights, 
■^^  being  the  average  probability  of  correctness  when  confident  for  ten  observers. 

*  Sixty  per  cent,  is  that  given  by  Pierce  and  Jastrow,  op.  cit. ;  Fullerton  and  Cat- 
tell give  60  and  65  per  cent,  for  two  observers,  op.  cit.,  132. 


CHAPTER   IV. 
The  Place  of  Stimulation. 

Sec.  I.   Previous  Investigations. 

In  our  study  of  the  accuracy  of  discrimination  we  con- 
fined our  experiments  to  a  definite  area.  It  has,  however, 
been  asserted  on  experimental  grounds  that  the  accuracy  of 
discrimination  varies  for  different  parts  of  the  body.  We 
shall  now  turn  to  this  aspect  of  the  question. 

The  so-called  tactile  sensibility  of  different  parts  has  gen- 
erally been  determined  by  Weber's  assthesiometer.  But  by 
this  method  the  spatial  sensibility  only  is  measured,  and  we 
are  not  justified  in  assuming  that  this  represents  the  general 
delicacy  of  the  peripheral  end  organs.  Perhaps  the  simplest 
method  of  testing  the  sensibility  of  different  parts  is  to 
determine  the  threshold  at  these  parts.  The  fact  that  the 
threshold  is  not  a  fixed  quantity  does  not  render  this  method 
impracticable.  Aubert  and  Kammler^  found  by  this  method 
that  there  was  but  little  difference  between  the  different  parts 
of  the  body.  The  face  was  somewhat  more  sensitive  and 
the  foot  less  sensitive  than  other  regions,  and  no  appreciable 
difference  appeared  between  the  sensitiveness  of  dorsal  and 
volar  surfaces.  The  results  were  quite  different  for  parts 
where  the  hairs  were  shaved.  Similar  results  were  obtained 
by  Bloch,^  according  to  whom  the  face  and  palm  of  the  hand 
were  more  sensitive  than  the  trunk,  arms  and  legs  when 
shaved. 

A  quite  different  method  was  used  by  Goltz,^  who  applied 
to  the  place  of  stimulation  the  end  of  a  rubber  tube  filled 
with  water,  the  other  end  being  applied  to  the  radial  artery. 
The  stimulus  was  the   periodic   pressure   from   the  arterial 

^  Aubert  and  Kammler,  op.  cit.     (See  Chap.  II,  Sec.  4.) 

'  Bloch,  op.  cit.     (See  Chap.  II,  Sec  4.) 

'Goltz,  Centralblatt  fur  die  Med.   IViss.,  1863,  273. 

47 


48  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

pulsations.  Goltz  concluded  that  the  sensitiveness  of  the 
skin  to  pressure  stimuli  varied  in  general  in  the  same  way  as 
the  discriminative  sensibility  for  space.  The  method  used 
is,  however,  extremely  unsatisfactory.  Not  only  was  no 
quantitative  determination  made,  but  possible  preconcep- 
tions could  not  but  influence  the  process  of  judgment. 
Goltz  was  led  to  the  use  of  such  a  method  by  observing  that 
a  branch  of  the  temporal  artery  can  be  easily  felt  with  the 
finger,  but  not  with  the  hand.  This  apparent  difference  in 
sensitiveness  is,  we  think,  at  least  partly  due  to  differences 
in  the  manner  of  applying  the  pressure.  It  is  much  more 
difficult  to  feel  the  arterial  pulsations  with  the  dorsal  than 
with  the  volar  surface  of  the  finger,  but  Aubert  and 
Kammler,  as  well  as  Bloch,  found  that  there  is  no  appre- 
ciable difference  in  the  sensitiveness  of  the  dorsal  and  volar 
regions. 

A  still  more  novel  method  is  that  of  Funke,^  who  tested 
the  sensitiveness  of  the  skin  by  applying  glycerine  solutions 
of  different  proportions.  That  solution  was  determined 
the  adhesiveness  of  which  could  be  just  distinguished  from 
that  of  pure  glycerine.  It  is  clear  that  the  accuracy  of  dis- 
crimination is  here  tested,  not  the  threshold,  and  that,  too, 
in  such  an  inexact  manner  that  accurate  quantitative  results 
would  be  impossible.  Besides,  the  stimulus  used  is  traction 
and  not  pressure,  and  as  would  be  expected,  the  results  are 
quite  different  from  those  obtained  by  others  for  pressure. 
Considering  the  inaccuracy  of  the  method  employed,  Funke's 
results  agree  fairly  with  those  of  Bloch, ^  for  traction  stimuli, 
the  order  of  sensitiveness  of  the  principal  parts  of  the  body 
being :  finger  tips,  palm  of  the  hand,  back  of  the  hand,  fore- 
arms, breast,  thigh,  feet  and  back. 

Results  quite  different  from  those  of  the  threshold  inves- 
tigators were  found  by  Schwaner^  and  also  by  Sergi,*  who 
determined  the  rate  of  vibration  of  a  tuning  fork  at  which 

^  Funke,  Fischers  Med.  Buchhandlung,  1891,  29,  as  quoted  in  Zeit.  fiir  Psy., 
Vol.  2,  399. 

"^  Bloch,  op.  cit. 

^  Schwaner,  Die  Prilfung der  Hautscnsibilitdt,  Dissert.,  Marburg,  1890,  as  quoted 
in  Zeit.  fiir  Psy.,  II,  398. 

*  Sergi,  Revista  di  Filosojia  Scientifica,  1891,  as  quoted  in  Zeit.  fiir  Psy.,  Ill,  175. 


THE  PLACE  OF  STIMULATION.  49 

the  tactile  sensations  began  to  fuse.  Schwaner's  results  are 
criticised  by  Sergi,  who  points  out  that  the  amplitude  of 
vibration,  and  consequently  the  intensity  of  the  stimulus,  is 
much  greater  for  forks  at  low  pitch.  Sergi  concludes  that 
we  measure  the  sensitiveness  of  the  different  parts  of  the 
skin  by  differences  in  the  intensity  of  the  stimulus  necessary 
to  cause  a  distinct  sensation.  It  is  probable  that  the  threshold 
element  enters  into  the  experiment,  as  Sergi  holds;  but  as 
the  results  are  quite  different  from  those  of  Bloch  and  Aubert 
and  Kammler,  it  is  not  improbable  that  local  differences  in  the 
duration  and  fusion  of  tactile  sensations  affect  the  results. 
Krohn^  states  that  dermal  after-images  last  much  longer  for 
some  parts  than  for  others. 

The  accuracy  of  discrimination  for  different  regions  was 
investigated  by  Weber^  and  also  by  Dohrn.^  Weber  applied 
weights  to  the  forearm,  and  found  that  the  increment  neces- 
sary in  order  to  be  appreciated  was  twice  as  great  as  when 
the  same  weight  was  applied  to  the  hand.  Weber  does  not, 
however,  mention  the  magnitude  of  the  stimuli  used.  Accord- 
ing to  Dohrn's  researches,  the  method  of  which  has  been 
described,  the  least  noticeable  difference  for  a  stimulus  of  i  g. 
was  smallest  for  the  thumb  and  fingers.  Then  follow  the 
hand,  forearm,  breast,  knee  pan  and  feet.  But,  as  we  have 
already  noted,  these  experiments  are  of  little  exact  value, 
since  not  only  is  the  method  open  to  serious  objections,  but 
the  experiments  were  made  by  the  observer  on  himself. 
Then,  too,  according  to  Aubert  and  Kammler,  individuals 
differ  not  a  little  in  the  relative  sensitiveness  of  different 
parts.  We  cannot  assume,  however,  even  if  these  results 
are  accepted,  that  the  absolute  accuracy  of  discrimination  is 
measured  for  different  places.  As  we  have  seen,  the  relative 
accuracy  of  discrimination  is  much  greater  for  stimuli  of 
moderate  intensity ;  consequently,  the  lower  the  threshold 
for  a  given  region,  the  greater  would  be  the  accuracy  of 
discrimination  at  this  region  for  low  intensities. 

'^Y^xo\v!\,  Journal  of  Mental  and  Nervous  Diseases,  March,  1893,  11, 
''Weber,  op.  cit.,  548.     See  Chap.  I,  Sec.  i. 
^  Dohrn,  op.  cit.     See  Chap.  Ill,  Sec.  i. 


§P  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

Sec.  2.  Further  Experiments :  the  Accuracy  of  Discrimination, 

The  writer  made  a  few  rough  experiments  on  the  thresh- 
old sensibility  of  the  hand,  arm  and  face,  by  the  instrument 
already  described,^  and  the  results  corroborated  those  given 
by  Bloch,  Aubert  and  Kammler,  as  well  as  Dohrn,  assuming 
that  the  latter's  results  were. due  to  the  threshold  differences. 
Experiments  were  also  made  on  the  discrimination  of  weights 
by  the  method  of  right  and  wrong  cases,  the  probable  error 
being  determined  for  different  parts.  Six  hundred  experi- 
ments were  made  on  N.  F.,  the  volar  surface  of  the  left  index 
finger,  third  phalanx,  being  the  place  of  stimulation.  The 
stimuli  used  were  50  g.,  200  g.  and  800  g.     The  average  of 

P  E 

the  six  values  of      '        obtained  was  -^,  which  was  approx- 

o. 

imately  the  same  as  that  obtained  for  the  palm  of  the  hand 
of  the  same  observer.^  Experiments  were  also  made  on 
L.  S.  The  stimulus  was  100  g.,  and  the  places  of  application 
were  the  volar  surface  of  the  left  index  finger  and  the  back 
of  the  hand.  The  probable  error  for  each  set  of  100  experi- 
ments is  given  below,  as  well  as  that  obtained  for  the  palm 
of  the  hand  at  the  same  time. 

^,  T-,  T-    c      r  P.E.  for  palm      P.E.  for  back 

Observer.     P.E.  for  finger.  ^^  ^^  J^^  ^^  ^^^  ^^^^^ 

L.  S.,  9.  16.  17. 

On  account  of  the  comparatively  small  number  of  experi- 
ments the  probable  errors  given  are  considerably  affected  by 
the  variable  error.  Making  allowance  for  the  variable  error, 
the  results  for  L.  S.,  taken  together  with  those  for  N.  F., 
indicate  that  apart  from  individual  variations  there  is  no 
very  marked  difference  in  the  accuracy  of  discrimination  for 
moderate  intensities  at  different  parts  of  the  hand. 

A  further  series  of  experiments  was  made  on  S.  F.  with 
5  g.  and  7  g.  as  the  stimuli.  The  volar  surface  of  the  index 
finger  and  the  hand,  and  the  dorsal  surface  of  the  forearm, 
were  the  places  of  stimulation.  In  these  experiments  the 
error  due  to  impact  is  constant  for  the  different  places,  and 

1  See  Chap.  II,  Sec.  4. 

»  See  Chap.  Ill,  Sec.  3.     Av.  ^^  for  N.  F.  is  |. 


THE  PLACE  OF  STIMULATION. 


51 


does  not,  therefore,  affect  the  relative  results.  Below  are 
given  the  probable  errors  for  the  different  sets  of  100  experi- 
ments. 


Finger. 

Hand. 

Wrist. 

Stimuli. 

Pi 

P. 

Ps 

Av. 
1.4 

Pi 

P, 

P3 

Av. 

Pi 

P, 

Ps 
2.3 

Av. 
4.9 

5  g-  and  7  g. 

1.3 

1.5 

1.5 

3.7 

1.8 

2. 

2.5 

9.1 

Z-Z 

These  experiments  show  that  for  5  g". -7g.  the  discrimi- 
nation is  somewhat  more  accurate  for  the  tip  of  the  finger 
than  for  the  palm  of  the  hand,  and  much  more  so  than  for 
the  back  of  the  fore  arm.  The  observer  improved,  however, 
greatly  from  practice  in  the  experiments  on  the  wrist.  As 
the  threshold  sensitiveness  is  here  much  less,  and  we  are  not 
accustomed  to  judging  stimuli  thus  placed,  the  difference 
was  to  be  expected. 


Sec.  3.    The  Inte7isity  of  the  Sensation. 

Another  method  of  investigating  the  sensitiveness  of 
different  places  is  by  comparing  the  intensive  q^qcX.  of  a  given 
stimulus  with  that  of  the  stimulus  applied  to  another  region. 
Weber  found  that  5  oz.  placed  on  the  finger  was  judged 
greater  than  4  oz.  on  the  arm,  but  when  the  weights  were 
reversed  they  were  judged  equal. ^  In  order  to  obtain  more 
accurate  results,  a  weight  of  5,  100,  or  1000  g,  was  applied 
to  the  finger,  and  upon  removal  applied  to  the  dorsal  surface 
of  the  wrist,  the  observer  being  required  to  judge  which 
seemed  heavier.  The  observers  were  ignorant  of  the  fact 
that  the  stimuli  applied  were  the  same.  If  in  10  experiments 
no  underestimation  of  the  stimulus  was  appreciable  at  one 
of  the  two  places  of  stimulation,  as  compared  to  the  other, 
we  concluded  that  any  difference  in  sensitiveness  was  too 
slight  to  be  considered.  When,  however,  the  answers  were 
such  that  the  weight  when  applied  to  the  wrist  was  consid- 
ered much  lighter,  increments  were  added  to  it  until  it 
seemed  equal  to  the  standard  weight  applied  to  the  finger. 
When  5  g.  was  used,  increments  could  not  be  conveniently 

^  Weber,  op.  cit. 


52 


SEATSAT/OA^S  FROM  PRESSURE  AN^D  IMPACT. 


added,  so  7  g.  and  10  g.  weights  of  the  same  area  were  used 
as  comparison  stimuli.  Below  are  the  results  for  four  ob- 
servers. The  values  of  the  increments  given  are  based  on 
five  experiments. 


Stimulus. 

Increments  added  on  wrist. 

P 

K 

L 

F 

lOOOg      -      -      - 
lOOg      -      -      - 

5g     -     -     - 

0 
>5 

0 
0 
0 

0 
0 

>2<5 

300 
90 

>2<5 

The  above  results  seem  to  show  that  there  is,  at  least  for 
low  intensities,  a  marked  underestimation  of  stimuli  applied 
to  the  arm,  in  comparison  with  stimuli  applied  to  the  finger. 
Observers  differ  greatly,  however,  that  this  cannot  be  stated 
as  a  universal  law,  K.  not  showing  any  appreciable  underes- 
timation. Possibly  these  individual  differences  may  be  due 
to  central  processes,  such  as  unconscious  allowance  for  sen- 
sory difference  in  comparing  the  stimuli.  The  fact  that  the 
underestimation  tends  to  diminish  for  high  intensities  goes  to 
show  that  different  regions  of  the  periphery  do  not  have  an 
intensity  coefficient  as  Weber  concluded. 

Sec.   4.    The  Pain  Threshold. 

By  the  algometer  already  described  the  writer  made  five 
measurements  of  the  pain  threshold  for  different  parts  of  the 
body.  But  one  measurement  for  a  given  place  was  made  at 
a  time..  Below  are  the  results  in  kilograms,  with  the  prob- 
able errors  of  the  averages. 

Top  of  the  head,  parietal  region.      -         -         -  1.8  ±.005 

Forehead,  frontal  region.    -         -         -         -  -     1.3^.008 

Breast,  over  sternum.       -         -         -         -         -  2.4  ±.006 

Abdomen.    --------  i.y  ±:.oo6 

Back.        -         - 8.0  dz.oio 

Right  temporal  region  of  head.    -         -         -  -     i.o±.oo3 

Left            "■             "'<....  1.3  j_,oo4 


THE  PLACE  OF  STIMULATION. 


53 


Right  thigh,  ventral  region.        -         -         -  -     4 

Left           an                 -'.-..  3 

Right  foot,  plantar  surface.          -         -         -  .     3 

Left         "         "           ''     -         -         -         -         -  3 

Right  heel.      "           "         -         -         .         -  -     7 

Left        "         ''           "      -         -         -         -      .  -  5 

Right  hand,  volar  surface.  -         -         -         „  .     7 

Left         "         "         "       -         -         -         .         -  6 

Right  hand,  dorsal  surface.*         -         -         -  -     3 

Left         *'          "           *•             -         -         -         -  3 

Right  index  finger,  volar  surface,  3d  phalanx..  -     3 

Left         **         "          "           **          "         "  '^ 


3  ±.oi 

2  dr. 007 
5  dr. 009 

4  ±.005 
b  dr.oo6 
9  ±:.OI 
3*ir.007 

2  ±:.007 

3  ±:.oo6 
6±.or 

5  ±:.oo6 


_.3  ±.006 

From  this  it  appears  that  the  regions  over  the  frontal 
and  temporal  bones  are  most  sensitive  to  pressure,  and  the 
heel,  the  back,  and  the  muscular  regions  of  the  leg  and  hand 
the  least  sensitive.  The  sensitiveness  to  pain  seems,  then,  to 
depend  largely  upon  the  thickness  of  the  skin  and  the  extent 
of  subcutaneous  tissues.  The  left  side  of  the  body  is  per- 
haps slightly  more  sensitive  than  the  right  side,  but  the  dif- 
ference, if  any  exists,  is  hardly  appreciable. 


*  The  measurements  on  the  hand  were  carried  on  simultaneously  with  the  others. 
But  quite  a  number  of  experiments  had  been  made  on  the  hand  before,  and  it  seemed 
to  have  become  less  sensitive  by  about  2  k.  than  when  it  was  first  tested. 


CHAPTER  V. 


Sensations  of  Impact. 

Sec.  I.    The  Threshold^  for  Touch.  • 

We  should  expect  a  priori  that  a  given  weight  would,  have 
^fedter  efifect  if  applied  with  appreciable  impact  than  if  impact 
Were  excluded.  In  order  to  find  if  such  were  the  case,  a 
circular  piece  of  cardboard  was  placed  carefully  upon  the 
hand  of  the  observer,  being  suspended  by  a  delicate  brass 
wire  about  i  cm.  long.  The  whole  weighed  .oig.  S.  F.  and 
the  writer  served  as  observers,  the  one  not  acting  as  observer 
placing  the  stimulus.  The  observer's  eyes  were  closed,  and 
he  did  not  know  when  the  stimulus  was  applied.  Fifty  ex- 
periments were  made  on  both  observers,  and  the  number  Of 
times  they  perceived  the  stimulus  was  recorded.  In  order 
td  compare  the  results  with  thdse  obtained  when  impact  was 
excluded,  the  pressure  was  applied  by  means  of  the  instru- 
ment described  in  Chap.  II,  Sec.  4.  In  order  to  have  the 
area  of  stimulation  constant,  the  pressure  was  exerted  upon 
the  card  piece  to  which  reference  has  just  been  made,  the 
projecting  wire  handle  having  been  removed.  The  pressure 
thus  applied  was  .4  g.  Below  are  given  the  percentage  of 
times  the  stimuli  was  felt  in  50  experiments. 


Impact. 

Pressure. 

.Gig 

•4g 

F. 
G. 
AV.       - 

56% 
52% 

54^- 

66% 
30% 
48% 

^W'e  retain  tbis  term  for  purposes  of  convenience,  there  being  no  other  to  denote 
stimuli  that  are  perceived  with  difficulty. 


■       ■"■■  SENSATIONS  OF  hlP ACT.  §§ 

It  is  evident  from  the  above  that  a  pressure  stimulus  has 
a  much  less  intensive  effect  than  one  of  impact,  even  if  the 
velocity  of  the  weight  applied  be  very  small.  If  the  preis- 
sure  were  applied  more  rapidly  (between  i  and  2  sec.  was 
the  time),  the  effect  upon  the  dermal  end  organs  would  be 
•more  marked.  But  the  quicker  the  increase  of  pressure 
the  more  would  its  effect  resemble  that  of  impact. 

Sec.  2.    The  Threshold  of  Pain. 

To  find  the  threshold  for  impact  stimuli  a  wooden  upright 
frame  was  constructed  i  m.  in  height.  A  box  containing  a 
weight,  of  lead  or  brass,  could  slide  in  an  open  groove  with- 
out appreciable  friction.  A  scale  showed  the  height  in  centi- 
metres through  which  the  box  fell.  The  part  of  the 
stimulus  in  contact  with  the  skin  was  of  wood  and  circular  iri 
shape,  the  diameter  being  i  cm.  The  box  was  allowed  td 
fall  by  the  hand,  after  being  raised  to  the  height  desired.  A 
wax  model  was  made  to  fit  the  hand  of  the  observer,  so  that 
when  the  hand  was  once  placed  under  the  movable  stimulus 
its  position  could  not  be  changed.  The  palm  of  the  hand 
was  the  place  of  stimulation.  By  means  of  this  instrument 
the  height  causing  pain  was  found  for  different  weights. 

The  experiment  was  conducted  as  follows.  The  required 
height  having  been  previously  found  very  roughly,  the 
weight  was  allowed  to  fall  from  a  height  somewhat  below 
this  point.  It  was  then  allowed  to  fall  from  a  height  5  cm. 
greater,  and  this  was  continued  until  pain  was  caused  by  the 
blow.  From  two  to  five  experiments  were  generally  made 
before  the  pain  threshold  was  recorded.  As  it  was  found 
that  repeated  trials  made  the  tissues  more  sensitive,  an  inter- 
val of  about  half  a  minute  elapsed  between  the  experiments.* 
Four  weights  were  used,  and  with  two  or  three  exceptions 
but  one  measurement  was  made  at  one  sitting  for  each  weight. 
The  order  in  which  the  heights  for  the  different  weights  were 
found  was  the  reverse  in  half  of  the  experiments  from  that 
which  was  followed  in  the  other  half.     Ten  experiments  for 

^  This  precaution  was  all  the  more  necessary  because  of  the  difference  in  times  of 
ahe  appearance  of  pain  and  the  sensation  of  impact.  This  difference  was  occasionally 
very  marked. 


$6 


SENSATIONS  FROM  PRESSURE  AND  IMPACT. 


each  weight  were  made  by  the  writer  upon  himself  and  five 
upon  L.,  an  advanced  student  of  psychology.  We  give 
below  the  average  values  in  centimeters  of  the  height  neces- 
sary to  cause  pain  for  the  different  weights  used.  The 
probable  errors  of  the  averages  are  also  given,  being  pre- 
ceded by  the  sign  it. 


Observer. 

25  g- 

50  g- 

100  g. 

300  g. 

L. 
G. 

32.8db  .5 
69.4^21.1 

i8.6±.4 
34.2±.3 

io.6±.3 
l6.8rt.i 

3.i±:.03 

5-4±:    .2 

If  we  multiply  the  above  values  for  the  height  by  the 
corresponding  weights,  we  obtain  the  following  results '} 

25  g. 

50  s:. 

100  g. 

300  g. 

L. 
G. 

820. ±12. 
1730.^27. 

930.  ±20. 
i7io.±i5. 

1060.  ±30. 
1680.  ±10. 

930.  ±9. 
1620.  ±60 

From  this  it  appears  that  the  product  of  the  weight  and 
the  height  necessary  to  cause  pain  is  fairly  constant.  Ex- 
pressing this  in  the  form  of  an  equation  we  have, 

Wh  =  k, 
which  is  the  equation  of  an  hyperbola.     If  for  Wh  we  sub- 
stitute its  value,  \  m  v',  we  have, 

I  m  v^  =  k, 
which  expresses  the  relation  between  the  mass  and  velocity 

necessary  to  cause  pain.     If  we  substitute  —  for  m,  we  have, 

v*  =  2k  m. 
This  equation  expresses  the  relation  of  the  velocity  and  the 
mass,  considered  as  factors  determining  the  intensity  of  the 
stimulus.  The  equation  is  that  of  a  parabola.  Its  meaning 
is  that  an  increase  of  the  square  of  the  velocity  has  the  same 
intensive  effect  on'  pain  sensations  as  a  corresponding  increase 
in  the  mass. 


^  The  probable  errors  of  these  results  are  found  by  multiplying  the  original  proba- 
ble errors  by  the  weights. 


SENSATIONS  OF  IMPACT.  $7 

By  taking  the  average  values  of  the  product  Wh  for  the  two 
observers,  and  comparing  these  with  the  average  values  of  the 
pressure  threshold  for  the  same  area,  we  find  that  for  L.  a 
pressure  of  about  2300  g.  is  equivalent  to  a  blow  of  the  same 
mass  through  a  height  of  4  mm.,  and  therefore  a  velocity  of 
28  cm.  per  sec. ^  For  G.,  in  like  manner,  the  pressure  of 
4500  g.  is  equivalent  to  a  blow  of  the  same  mass  having  a 
velocity  27  cm.  per  sec.  For  velocities  less  than  these 
greater-masses  would,  according -to ;  theory,  be  required  for 
impact  than  for  pressure.  It  is  probable,  therefore,  that  the 
equation  does  not  hold  for  very  low  velocities.  This  we 
might  naturally  expect,  since  as  the  velocity  decreases  the 
less  is  the  difference  between  impact  and  pressure  stimu- 
lation. 

Sec.  3.     The  Analysis  of  Mass  and  Velocity  in  Impact  Stimuli, 

When  the  same  weight  falls  upon  the  skin  from  different 
heights,  different  sensations  are  aroused.  In  order  to  inves- 
tigate the  subjective  effects  of  mass  and  velocity  in  haptic 
sensations  proper,  as  opposed  to  those  of  pain,  the  writer 
allowed  a  weight  of  100  g.  to  fall  upon  the  palm  of  the  ob- 
server's hand  from  a  height  of  5  cm.,  in  the  manner  already 
described,  and  then  found  the  approximate  height  at  which 
a  weight  of  25  g.,  and  the  same  area,  seemed  to  give  rise  to 
a  sensation  of  equal  intensity.  That  height  was  considered 
the  height  required,  at  which,  in  ten  or  more  trials,  about 
half  of  the  observer's  judgments  were  '  heavier  '  and  half 
*  lighter.'  When  the  experiments  were  begun,  the  observers 
were  asked  to  judge  which  weight  seemed  heavier  or  lighter 
rather  than  which  seemed  to  give  the  more  intense  sensation. 
It  was,  however,  evident  from  the  statements  made  by  the 
observers  that  they  judged  the  intensity  of  the  blow.  Some 
spoke  of  a  difference  in  the  quality  of  the  sensations,  and  two 
said  that  the  weights  fell  with  different  velocities.  We  give 
below  the  heights  determined  for  different  observers  at  which 
the  blow  of  25  g.  seemed  equal  to  that  of   100  g.  at  5  cm, 

^  The  velocity  is  readily  calculated  from  the  height  by  the  formula,  h  =    — ^ 


58 


SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 


We  give  also  the  square  roots  of  the  heights,  since  these. 
may  be  taken  to  represent  the  velocities. 


Observer. 

.  S.  F. 

L.  F. 

L. 

K. 

P.  , 

h. 

40 

40 

58 

33 

2b 

I  k: 

6.^3^ 

6.3 

7.6 

5-.  7 

4.5 

The  individual  differences  are  so  great  that  an  exact 
inference  is  impossible.  It  is,  however,  evident  that  in  order 
that  blows  be  judged  of  equal  intensity,  the  height,  or  the 
square  of  the  velocity,  has  in  general  much  less  effect  than 
the  weight.  For  if  this  were  not  the  case,  the  average 
height  for  25  g.,  to  cause  a  blow  judged  equal  to  that  from 
100  g.  at  5  cm.  would  be  not  far  from  20  cm.^  On  the  other 
hand  the  velocity  appears  to  have  a  relatively  greater  effect 
than  the  mass.  Otherwise  the  average  values  of  v^h  for 
:25  g.  would  be  approximately  8.8  cm.  or  more.^  If  we  assume 
that  the  above  judgments  are  based  upon  equality  of  sensory 
intensity,  we  may  conclude  that  to  cause  an  intensive  effect 
equal  to  that  of  the  velocity,  the  mass  must  increase  faster 
than  the  velocity,  but  more  slowly  than  the  square  of  the 
velocity.  The  great  individual  variations  make  it  probable, 
however,  that  the  process  of  judgment  is  somewhat  complex. 
Possibly  the  fact  that  we  are  more  accustomed  to  judge 
w^eights  than  velocities,  may  partly  account  for  the  difficulty 
observers  have  in  forming  a  judgment.  Then,  too,  the 
change  in  sensation  due  to  velocity  is  of  different  modality 
from  that  due  to  weight.  But  although  we  cannot  assume 
that  a  relation  is  obtained  between  the  intensive  effects  of 
mass  and  velocity,  this  is  extremely  probable.  The  com- 
plexity of  the  processes  of  comparison  is  such  that  great 
individual  variations  are  to  be  expected ;  but  to  whatever 
extent  the  judgments  be  affected  by  non-peripheral  pro- 
cesses, they  are  doubtless  based  upon  differences  in  sensory 
intensity. 

*  100  g.  X  5  cm.  =  25  g.  X  20  cm. 

•  100  g.  X  2.2  cm.  =  25  g.  X  8.8  cm. 


SENS  A  TIONS  OF  IMP  A  CT.  J  9 

Sec.  4-    The  Discrimination  of  Mass  and  Velocity. 

In  order  to  investigate  the  accuracy  of  discrimination  for 
impact  stimuli,  an  apparatus  was  used  constructed  as  shown 
in  the  cut. 


Fig.  7. 


An  aluminium  bar,  AB,  movable  vertically,  was  attached 
to  a  horizontal  axis,  B,  so  that  it  could  fall  from  different 
angular  elevations.  At  the  extremity  of  the  bar  weights  of 
brass  or  lead  could  be  attached.  Metallic  upright  bars, 
attached  to  the  wooden  base,  DF,  GH,  were  provided  with 
movable  clamps,  L  and  M.  On  these  clamps  catches  were 
fitted  by  which  the  experimenter  could  let  the  weight  and 
bar  fall  from  any  desired  angular  elevation.  When  a  con- 
stant height  was  used,  it  was  more  convenient  to  let  fall  the 
weight  from  an  electro-magnet,  T.  A  scale  furnished  the 
means  of  adjusting  the  angular  elevations.  The  stimulus 
was  applied  to  the  palm  of  the  left  hand,  which  was  placed 
in  a  wax  rest  made  to  fit  the  hand.  The  hand  was  in  contact 
with  the  cylindrical  piece,  K,  projecting  from  the  extremity 
of  the  weighted  aluminium  bar  when  the  bar  was  horizontal. 

Two  different  sets  of  experiments  were  made.  In  one  of 
these  the  mass  applied  was  variable  and  the  velocity  con- 
stant. In  the  other  the  mass  was  constant,  the  observer 
being  required  to  estimate  differences  in  the  intensity  of  the 
blow  from  increments  in  velocity  due  to  height.  If  K  de- 
note the  moment  of  inertia  of  the  falling  mass,  o)  the  angular 
velocity,  W  the  weight,  v  the  linear  velocity,  h  the  height 


6d  SENSA  TIONS  FROM  PRESSURE  AND  IMP  A  CT. 

through  which  the  centre  of  gravity  fallSj  and  r  the  distance 
from  the  axis  to  the  centre  of  gravity,  we  have 

^  K  0)'  =  Wh^ 
and 

^  K  r»  v«  =  Wh. 
Since  K  r*  is  constant,  when  the  height  only  is  variable, 

V  =  c  /h. 
Hence  we  may  take  \/h  to  represent  the  velocity  when  the 
height  is  varied.  This  quantity  is  takep,  as  ...the  .stimulus 
when  the  mass  is  constant,  the  weight  being  allowed  to  fall 
successively  from  different  heights,  and  the  accuracy  of  dis- 
crimination being  measured  by  the  method  of  right  and 
wrong  cases.  In  order  that  the  judgment  might  be  based 
upon  the  sensation  of  impact  only,  the  writer  caught  the 
lever  arm  of  the  weight  by  the  hand  the  moment  after  it 
struck  the  observer's  hand.  As  there  was  a  slight  rebound, 
it  was  thus  comparatively  easy  to  eliminate  pressure  sensa- 
tions. The  values  of  h  for  different  values  of  the  angular 
elevation  of  the  lever  arm,  ^,  were  calculated  by  the  formula 
deduced  for  the  purpose, 

h  =  r  sin  {6  ^  a)  —  /, 
in  which  a  represents  the  angle  betwen  the  lever  arm  and  the 
line  passing  from  the  axis  of  rotation  to  the  centre  of  gravity 
of  the  lever  arm  and  weight,  C,  and  /represents  the  distance 
from  C  to  the  lever  arm.  The  position  of  C  was  found  by 
experiment.  The  above  formula  was  roughly  verified  by 
measurements  which,  on  account  of  the  position  of  C,  were 
too  inexact  to  serve  as  a  basis  for  calculations. 

In  the  experiments  the  results  of  which  are  given  below 
the  standard  weight  was  50  g.  Two  standard  heights  were 
used,  5.4  cm.  and  17.5  cm.  The  increments  were  for 
height  1.3  cm.  and  3.5  cm.,  and  for  weight  10  g.  The  per- 
centage of  right  answers  varied  generally  between  70%  and 
90%.     In  the  tables  appended  are  given  the  probable  errors 

^  For  the  deduction  of  this  formula,  the  writer  is  indebted  to  Prof.  R.  S.  Wood- 
ward, of  Columbia  College.     If  F  be  the  impressed  forces,  r  the  lever  arm,  and  6  the 

d'  0 
angular  elevation,  K  -j-j  =  Fr  =  Wr  cos  6.     Hence, 


dt 
dt 


K      I  ^  de  =  Wr  sin  6  =  Wh  =  i  K  «^ 
J  dt*  ^ 


SENSA  TIONS  OF  IMPACT. 


6i 


for  the  different  sets  of  lOO  experiments.^  The  second  col- 
umn indicates  the  nature  of  the  variable  stimulus,  whether 
weight,  W,  or  velocity,  -v/h.  When  the  variable  stimulus  is 
the  weight,  the  probable  error  is,  of  course,  in  terms  of 
weight.  When  the  variable  stimulus  is  velocity,  the  prob- 
able error  is  calculated  in  terms  of  -/h.^     In  the  sixth  col- 

p 

umns  are  given  the  values  of  -^,  the  average  probable  error 

o 

divided  by  the  mean  of  the  two  stimuli  compared.     In  the 

P 

last  columns  are  the  values  of  ^  for  velocity,  Rv,.  divided  by 

o 

p 

^  for  weight,  Rw.     This  indicates  the  ratio  of  the  accuracy 

of  discrimination  for  velocity  to  that  for  weight. 
H  =  5.4  cm.  H  -\-  AH  =  6.7  cm. 
VH  =  2.32  cm.  v  H  -f  AH  =  2.58  cm. 


Observer. 

Var.  S. 

Pi 

P. 

Av.  P. 

P 

S 

=  R. 

Rv 
Rw 

S    F. 

W  =  50  g. 

6.5 

8.0 

7.2 

.13 

=  Rw. 

8 

v/h  =  2.32  cm. 

.33 

•25 

.29 

.12 

=  Rv. 

L.  F. 

W  =  50  g. 
v/h  =  2.32  cm. 

5.9 
.  12 

— 

5-9 
.12 

.11 

.05 

=  Rw. 
=  Rv. 

.4 

H  =  17.5  cm.  H  +  AH  =  21.  cm. 
l/H  =  4.19  cm.  -/H  +  AH  =  4.58  cm. 


Observer. 

Var.  S. 

Px 

P, 

Av.  P. 

P 

S  =  R. 

Rv 
Rw 

S.  F. 

W  =  50  g. 
\/h  =  4.19  cm. 

4.2 

•43 

6.7 

•43 

5^4 
•43 

.  10  =  Rw. 
.10  =  Rv. 

I.O 

L.  F. 

W  =  50  g. 
\/h  =  4.19  cm. 

5- 
.23 

3-9 

•27 

4-4 
.25 

.o8  =  Rw. 
.o6  =  Rv. 

.7 

L. 

W  =  50  g. 
\/h  =  4.19  cm. 

6.3 
.73 

7-7 
.60 

7.0 
.66 

.13  =:  Rw. 

.15=  Rv. 

I.I 

^See  Chap.  Ill  for  method  of  calculation.  The  prob.  errors  are  not  here  cor- 
rected as  in  Chap.  III. 

»  When  the  weight  is  varied  there  is  a  slight  change  in  the  velocity.  For  a  small 
increment  of  weight,  however,  this  may  be  neglected,  as  will  be  seen  from  the  formula, 
^  Kw*  =  Wh. 


62  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

In  order  to  compare  the  accuracy  of  discrimination  for 
blows  with  that  for  pressure  stimuli,  400  experiments  on  S. 
F.  and  L.  F.  were  made  with  a  weight  of  1000  g.  and  an  area 
approximately  the  same  as  that  used  in  the  impact  experi- 
ments. We  give  below  the  mean  of  the  two  probable  errors 
obtained  for  S.  F.  and  for  L.  F.,  divided  by  the  mean  of  the 

F  P 

stimuli  compared,  ^.    The  values  of  -^  for  50  g.  are  also  given 

for  comparison.  These  are  for  the  greater  height  17.5  cm., 
since,  in  order  to  have  a  logical  basis  of  comparison,  it  is 
necessary  to  compare  the  relative  probable  errors  at  inten- 
sities not  greatly  differing.  Weber's  law,  we  have  seen,  holds 
approximately  only  for  moderately  high  intensities.  This  is 
moreover  evident  from  the  table  since  the  relative  probable 
errors  at  the  two  heights  are  appreciably  different. 

P  P 

^^  for  pressure,  -^  for  impact. 

S.  F.  ^  1000  g.  ^ig.  50  g.  X  17-5  cm. 
T     F     1  1 

From  the  results  given  above  we  may  conclude,  first  that 
there  is  no  marked  difference  in  the  accuracy  of  discrimina- 
tion for  pressure  and  for  impact,  and  second,  that  the  dis- 
crimination for  velocity  tends  to  be  more  accurate  than  that 
of  weight.  If,  however,  instead  of  calculating  the  probable 
errors  for  the  square  root  of  the  height,  we  had  calculated 
them  for  the  height,  which  represents  the  energy  of  the  blow, 
we  should  have  found  that  the  discrimination  was  better  for 
the  mass  than  the  height.  This  difference  in  the  discrimina- 
tion for  mass  and  velocity  may  be  due  to  processes  of  percep- 
tion or  to  actual  differences  in  the  intensive  effects  of  mass 
and  velocity.  If  we  assume  that  the  latter  explanation  is  the 
true  one,  we  can  say  that  in  order  to  produce  equal  sensory 
effects  the  relative  increments  of  mass  and  velocity  are  related 
as  expressed  by  the  equation, 

Av  Am 

v  m 

Rv 

m  which  k  is  a  constant,  having  the  same  value  as  p—  in  the 


SENSATIONS  OF  IMPACT.  63 

tables.     If  this  equation  hold,  whatever  be  the  values  of  Am 

and  Av,  we  have, 

dv      -    dm 

v  m 

whence,  by  integration, 

log.  C  4-  log.  V  =r  k  log.  m, 

in  which  log.  C  may  be  taken  as  the  constant  of  integration. 
From  this  we  have, 

C  V  =  m^ 
or, 

V  =  Cm''. 

Rv 
Substituting  for  k  the  average  of  the  values  of  -^ — , 

Rw 

v  =  C'miny. 

That  is,  the  velocity  increases  as  mrV.  As  it  is  more  con- 
venient to  take  the  mass  as  the  most  direct  factor  in  the  in- 
tensive  effect  of  the   stimulus,   the  above   relation  may  be 

expressed, 

m  =  C'V-3 

We  may,  therefore,  write  as  the  intensive  stimulus  in  im- 
pact, S, 

S  =  mv^-3 

The  quantity  k  is  so  difficult  to  determine,  whether  or  not 
it  be  variable  for  individuals,  that  the  above  expression  is 
only  approximate.  It  is,  however,  clear  that  the  stimulus  is 
to  be  judged  a  quantity  varying  between  the  momentum  mv, 
and  the  kinetic  energy,  mv^.  In  other  words  the  mass 
has  greater  intensive  effect  than  the  energy  due  to  the  veloc- 
ity, but  less  effect  than  the  velocity. 

It  is  possible  that  the  results  obtained  are  dependent 
entirely  on  the  processes  of  comparison  and  judgment.  The 
conclusion  at  which  we  arrived,  assuming  this  not  to  be  the 
explanation,  is  the  same  as  that  which  we  reached  in  the  ex- 
periments on  the  direct  comparison  of  the  intensive  effects  of 
mass  and  velocity.  It  seems,  therefore,  preferable  to  con- 
sider the  complex  central  process  involved  as  causally 
related  only  to  the  great  individual  variations.  It  is,  never- 
theless, not  to  be  assumed  that  these  variations  are  entirely 


64  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

of  central  origin.  They  may  be  due  to  differences  in  the 
sensitiveness  of  the  dermal  nerves  to  impact  stimuli.  The 
problem  becomes  still  more  complex  in  view  of  the  fact  that, 
as  we  have  found,  the  pain  threshold  is  determined,  approxi- 
mately at  least,  by  the  kinetic  energy  of  the  blow.  This 
might  be  explained  teleologically  in  that  the  injury  done  to 
the  organism  would  tend  to  vary  as  the  energy  of  the 
blow.  If,  as  we  think  probable,  dermal  pain  is  a  distinct 
sensation,  with  perhaps  a  distinct  anatomical  and  physiolo- 
gical basis,  it  is  not  surprising  that  its  stimulus  should  be 
different  from  that  for  impact  sensations  proper. 


CHAPTER   VI. 

The  Area  of  Stimulation. 

Sec.  I.    The  Area  of  Stimulation  and  Judgments  of  the  Inten- 
sity of  the  Stimulus. 

It  is  a  common  experience  that  a  needle  or  other  stimulus 
acting  on  a  small  dermal  area  will  cause  pain,  when  the  same 
pressure  applied  to  a  large  area  will  not.  The  intensity  of 
haptic  sensations  appears,  therefore,  inversely  related  to  the 
area  of  stimulation.  For  the  study  of  this  problem  different 
methods  were  used,  the  first  of  which  will  now  be  described. 

Boxes  constructed  as  described  in  Chapter  III,  Sec.  2, 
were  applied  successively  to  the  volar  surface  of  the  left 
hand,  and  the  observer  was  required  to  say  which  seemed 
the  heavier.  The  area  of  one  of  the  bases,  which  were 
circular,  was  8  sq.  cm.,  that  of  the  other  was  .12  sq.  cm. 
approximately,  that  is  -J^  of  the  larger  area.  For  conven- 
ience we  shall  speak  of  the  larger  area  as  A,  and  that  of  the 
smaller  as  a.  Two  sets  of  experiments  by  the  method  of 
right  and  wrong  cases  were  carried  on  simultaneously.  In 
one  set  an  increment,  which  we  shall  call  A^,  was  added  to 
the  box  A^  weighted  to  200  g.,  so  that  a,  weighted  to  200  g., 
was  generally  judged  the  lighter.  In  this  set  A  was  always 
the  first  to  be  applied.  In  the  other  set  a  different  increment 
(A2)  was  added  to  A,  such  that  y4  4-Aj  was  generally  judged 
lighter  than  a.  In  this  series  a  was  always  the  first  to 
be  given.  In  this  way  the  observer  could  not  be  influenced 
by  the  association  of  one  area  with  an  apparently  greater 
intensity. 

The  method  of  calculating  the  overestimation  of  the  in- 
tensity of  a  is  as  follows. 

Let  C.E.  be  the  constant  error  due  to  overestimation  of 
the  second  of  two  stimuli,  P.E.   the  probable  error,  Tj^  and 

65 


66  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

Tj  the  values  of  the  probability  integral  corresponding  to  the 
percentages  the  second  stimulus  is  judged  heavier  and 
lighter,  and  N,  the  required  constant  overestimation  of  the 
stimulus  acting  on  the  smaller  area.  Then  for  the  series 
A-{-\  as  first,  and  a  as  second  stimulus,  from  the  formula, 

A 

=  T 

P.E.         »'' 

C.E.  +  N— A,       _, 

we  have,  5-- =  ^j, 

r  .Cj. 

whence,  N=T^  P.E.  +  A^— C.E. 

For  the  series  a  as  first,  and  A-\-i^2  ^^  second  stimulus,  we 


have, 


N— C.E.— A2_ 


Observer,  W, 

N, 

N, 

N3 

N. 

Av.N 

Stimulus,  200  g., 

65 

68 

75 

69 

69 

P.E. 
whence,  N=T,  P.E+Aj+C.E. 

The  values  of  P.E.  and  C.E.  having  been  found  by  ex- 
periments carried  on  simultaneously  with  these,  the  values 
of  N  were  calculated  from  the  above  equations.  With  W., 
an  advanced  student  of  psychology,  400  experiments  were 
made,  and  the  values  of  N  for  each  set  of  100  were  as 
follows : 

S 
1/3 

The  overestimation  of  the  weight  applied  to  about  -^^  of 
the  larger  area  was,  therefore,  approximately  ^  of  the  stimu- 
lus. Experiments  were  also  made  by  another  method,  and  on 
a  number  of  observers.  The  method  of  right  and  wrong  cases 
was  used,  but  the  relations  of  the  stimuli  were  different. 
The  first  stimulus  was  constant,  and  had  the  smaller  area. 
The  second  stimulus  was  part  of  the  time  A  +  A^  and  part  of 
the  time  A-\-^^,  the  values  of  Aj  and  Aj  being  such  that 
y^+Ai  was  judged  heavier  and  ^-f  ^2  lighter  than  a,  the  con- 
stant first  stimulus.  By  this  method  from  twenty  to  fifty 
experiments  were  made  on  W.,  N.  F.,  L.  S.,  and  McW.,  all 
being  subjects  in  the  experiments  on  discrimination  of 
weights  already  described.     Not  enough  experiments  were 


THE  AREA   OF  STIMULA  TION.  67 

made  to  base  a  calculation  upon  them,  but  enough  to  esti- 
mate roughly  the  overestimation.  The  results  for  W.  were 
corroborative  of  those  already  obtained,  both  for  100  g.  and 
200  g.  L.  S.  and  McW.  showed  an  overestimation  at  500  g. 
of  about  -L  the  stimulus,  closely  corresponding  to  that  of  W. 
N.  F.  showed,  however,  an  appreciable  tendency  to  under- 
estimate the  weight  of  a  2A.  100  g.  and  also  at  200  g. 

By  a  third  method  the  increment  added  to  a  weight  with 
area  A  pressing  on  the  hand  in  order  to  make  it  appear  equal 
to  the  same  weight  lifted  w^as  compared  to  the  increment 
which  had  to  be  added  when  the  area  was  a  instead  of  A, 
Below  are  the  values  of  the  increments  obtained  for  a  200  g. 
weight,  each  based  upon  five  or  more  experiments.  The 
observers  were,  of  course,  ignorant  of  the  purpose  of  the 
experiment,  as  well  as  of  the  magnitude  of  the  increments. 


P. 

K. 

L.F. 

S.F. 

A. 

37 

0 

150 

148 

a. 

0 

0 

0 

140 

In  only  two  of  the  four  observers  does  this  overestimation 
due  to  the  area  appear  very  marked  in  these  experiments. 
From  this,  and  from  the  fact  that  by  a  different  method  there 
was  not  only  no  overestimation  found  for  N.  F.,  but  even 
the  reverse,  we  may  conclude  that  this  constant  tendency  is 
by  no  means  universal. 

The  fact  that  individual  variations  are  such  that  we  can- 
not infer  a  relation  between  the  area  and  the  intensity  of 
stimulation  does  not  prove  that  such  a  relation  does  not 
exist.  An  observer  may  unconsciously  allow  for  this  over- 
estimation  in  his  judgment,  though  this  was  certainly  not 
the  case  with  N.  F.,  since  this  observer  supposed  the  larger 
area  would  seem  heavier.  It  is  difficult,  moreover,  to 
explain  in  this  way  the  results  obtained  by  the  last  method. 
But  in  the  direct  comparison  of  weights  of  different  areas, 
great  difficulty  is  experienced  by  some  observers  in  forming 
a  judgment.  The  sensations  seem  heterogeneous  and  there- 
fore incomparable.  It  is  only  by  abstraction  that  a  judgment 
of  intensity  is  possible ;  and  in  this  process  it  is  but  natural 
that  individuals  should  differ  greatly. 


68 


SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 


Sec.  2.    The    Tactile    Threshold. 

If  the  intensity  of  haptic  sensations  is  related  to  the  area 
of  stimulation,  we  should  expect  the  tactile  threshold  to  vary 
with  the  area.  For  the  purpose  of  investigating  this  prob- 
lem, the  writer  cut  circular  pieces  of  card  board  about  3.5 
mm.  and  10.7  mm.  in  diameter,  their  areas  being,  therefore, 
approximately  in  the  ratio  i  :  9.  The  weights  of  the  cards 
were  about  .01  g.  and  .05  g.  ;  but  this  may  be  neglected, 
since  only  at  the  moment  of  application  of  the  weight  do 
pressure  stimuli  of  low  intensity  have  any  sensory  effect. 
When  one  or  both  of  these  cards  had  been  placed  on  the 
palm  of  the  hand  of  the  observer,  who  was  blindfolded,  the 
pressure  necessary  to  affect  consciousness  was  found  by  the 
apparatus  and  methods  described  in  Chapter  II.  The  same 
corrections  are  also  made.  Ten  experiments  for  each  area 
were  made  on  L.  F.  by  the  writer,  and  as  many  on  the  writer 
by  S.F.,  who  was  carefully  instructed  as  to  the  precautions 
necessary.  A  third  set  of  experiments  was  made  in  which 
no  card  was  used,  the  pressure  being  exerted  directly  upon 
the  skin  by  the  vertically  projecting  bristle  of  the  instru- 
ment. The  diameter  of  the  bristle  being  about  .4  mm.  the 
area  applied  was  about  1.2  mm.  Below  are  the  results  in 
grams  for  each  group  of  ten  experiments. 


S.  F. 

H.  G. 

Area. 

Av. 

Max. 

Min. 

Av. 

Max. 

Min. 

I  mm. 

.2 

•5 

.  I 

•5 

I. 

.2 

ID  mm. 

•9 

1-7 

•3 

1.4 

3-2 

•3 

90  mm. 

1.9 

2.7 

I. 

1.6 

2.5 

•4 

It  appears  from  this  that  the  tactile  threshold  varies  with 
the  area  of  stimulation,  but  that  it  increases  much  more 
slowly  than  in  direct  proportion.  From  what  we  have  already 
said  regarding  the  possibility  of  regarding  the  threshold  as 
a  definite  quantity  more  exact  results  could  hardly  be  ex- 
pected. Strictly  speaking  we  are  not  justified  in  using  the 
term  threshold,  but  it  is  convenient  to  do  so,  if  we  bear  in 
mind  that  no  absolute  quantity  is  measured,  but  only  the 
relative  sensory  effect  of  stimuli  acting  on  different  areas. 


THE  AREA   OF  STIMULA  TION.  69 

Sec.  3.    The  Threshold  of  Pain. 

In  order  to  investigate  this  relation  with  accuracy, 
wooden  cones  of  hard  wood  were  cut  across  vertically  by  a 
lathe  at  three  points  so  determined  by  calculation  that  the 
diameters  of  the  sections  would  be  approximately  6.18  mm., 
10.70  mm.,  and  18.54  mm.  A  still  smaller  circular  base, 
about  3.56  mm.  in  diameter,  was  made  by  rotating  a  wooden 
cone  cut  by  hand  over  sand  paper  until  the  diameter  required 
was  obtained.  In  this  way  areas  were  obtained  of  approxi- 
mately 10,  30,  90,  and  270  sq.  mm.  The  diameters  of  the 
two  smaller  bases  were  measured  a  number  of  times  on  the 
dividing  engine.  The  averages  of  five  readings  were  6.21 
cm.  and  3.58  cm.,  which  shows  that  the  areas  are  sufficiently 
accurate.  In  applying  the  pressure  the  algometer  already 
described  was  used.  The  pressure  was  exerted  upon  the 
desired  area  by  fitting  the  upper  part  of  the  wooden  piece,  the 
base  of  which  had  the  area  in  question,  into  another  wooden 
piece.  Into  this  in  turn  could  be  fitted  the  projecting  cap  of 
the  algometer.  The  rate  of  increase  of  the  pressure  was 
kept  as  constant  as  possible,  and  this  was  as  great  as  was 
consistent  with  taking  the  readings  accurately.  The  error 
due  to  the  increase  of  pressure  between  the  appearance  of 
the  pain  and  the  taking  of  the  reading  is  corrected  as  in 
Chapter  II.  It  will,  therefore,  not  affect  the  results.  The 
place  of  stimulation  was  the  palm  of  the  hand.  With  F.  the 
right  hand  was  used,  but  the  left  hand  was  used  in  experi- 
ments on  G.  But  four  experiments  were  made  on  one  day, 
one  for  each  area.  In  half  of  the  experiments  the  order  in 
which  the  different  areas  were  used  was  the  reverse  of  that 
which  was  followed  in  the  other  half.  Though  the  experi- 
ments made  by  the  writer  on  himself  were  purposely  extended 
over  several  weeks,  a  gradual  decrease  of  sensitiveness  to 
dermal  pain  was  observed.  This  is  not  so  noticeable  in  the 
results  found  for  S.  F.  The  averages,  with  their  probable 
errors,^  are  given  below,  for  each  set  of  five  experiments. 
The  figures  indicate  kilograms. 

^  As  the  quantity  determined  increases  appreciably  for  G. ,  the  use  of  the  probable 
error  is  not  justified,  and  it  is  not  given. 


70 


SENS  A  TIONS  FROM  PRESSURE  AND  IMPACT. 


Observer, 

Group. 

Area, 

.  I  cm. 

.3  cm. 

.9  cm. 

2.7  cm. 

S.  F. 

ist  five.     '\   i.4=L..o 
2nd  five.    !   i.Qzt.  i 

2.7. Izh 
2.7.zbl 

3.   db.i 
3.4±.i 

4.5d=.2 
4.8±.2 

G. 

ist  five. 
2nd  five. 

I. 
1-3 

2.6 

3-1 

4.6 
6.8 

7-3 
10. 

Av. 

1.4 

2.8 

4.4 

6.6 

These  results  are  represented   graphically  in    the  accom- 
panying curves. 

FIGURE  3. 


Tntens- 


/Irea 


\o  30 


90 


tlQ 


As  the  curves  obtained  differ  somewhat,  it  is  impossible 
to  express  the  relations  by  a  simple  expression.  They  ap- 
proximately are  logarithmic  curves,  but  for  the  largest  area 
the  increase  of  intensity  is  too  great.  As  the  stimuli  are 
in  geometrical  progression,  the  logarithmic  relation  requires 
an  arithmetical  increase  of  the  area.  We  may,  therefore, 
test  the  results  by  finding  the  differences  between  the  thresh- 
old at  the  different  areas.     These  differences  are  as  follows: 

30  and  90  mm.      90  and  270  mm. 

3  1-5 

.7  1.4 

.0  2.7 


10 

and  30  mm 

S.  F. 

1-3 

S.  F, 

.8 

G. 

1.6 

G. 

1.8 

Av. 

1-3 

2.2 


The  increments  appear  to  increase  with  the  area,  whereas 
an  arithmetical  progression   requires  that  they  be  constant. 


THE  AREA   OF  STIMULATION.  %! 

But  as  will   be  seen  by  inspection  of  the  above  figures,  the 
increase  is  within  the  limit  of  individual  and  other  variations. 

Sec.  4.    Theoretic  Interpretation  of  Experiments  on  the  Intensive 
Effect  of  the  Area. 

We  have  by  three  entirely  different  methods  investigated 
the  intensive  effect  of  the  area  of  stimulation.  By  each  one 
of  these  methods  we  have  arrived  at  the  same  result,  that 
the  intensity  of  pressure  sensations  is  inversely  related  to 
the  area  of  stimulation.  We  have  seen  that  the  intensity 
causing  pain  is  approximately  proportional  to  the  logarithm 
of  the  area.  Hence,  as  the  intensity  of  the  stimulus  increases, 
its  effect  is  the  same  as  that  from  the  decrease  of  the  corre- 
sponding logarithm  of  the  area.  The  experiments  on  the 
tactile  threshold  and  on  judgments  of  intensity,  though  not 
admitting  of  such  an  interpretation,  nevertheless  seem  to 
show  that  the  intensity  threshold  increases  much  more  slowly 
than  the  area.  Hence  we  may  write  as  an  approximate 
expression  of  the  relation  between  the  intensity  and  the  area 
of  the  stimulus  which  must  exist  in  order  that  equal  subjec- 
tive intensive  effects  be  produced, 

1=  -JL 

log  A 
If  we  could  assume  Fechner's  law  we  could  substitute  the 
value  of  I  in  the  equation, 

S  =  K,  log  I, 
in  which  S  denotes  intensity  of  sensation,  and  obtain, 

S  =  K,log(j^). 

That  is,  the  intensity  of  the  sensation  increases  as  the 
logarithm  of  the  reciprocal  of  the  logarithm  of  the  area 
multiplied  by  a  constant.  If,  as  Hering  and  some  others 
hold,  S  is  directly  related  to  I,  the  relation  between  S  and 
A  would  be  an  inverse  logarithmic  one.  If,  as  the  majority 
of  psycho-physicists  believe,  S  increases  much  more  slowly 
than  I,  even  though  not  in  logarithmic  proportion,  it  would 
increase  correspondingly  more  slowly  than  the  reciprocal  of 
the  logarithm  of  the  area.     The  inverse  relation  here  exist- 


72  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

ing  is  contrary  to  what  we  might  expect  by  the  analogy  of 
other  senses.  In  the  case  of  temperature  sensations  Weber 
showed  that  the  intensity  increased  with  the  area.^  Miiller— 
Lyer  found  that  the  least  noticeable  difference  for  visual 
stimuli  increased  with  the  area  of  stimulation  in  about  the 
same  proportion  as  when  the  intensity  was  variable  and  the 
area  constant.^  With  pressure  stimuli  the  conditions  are 
apparently  the  same ;  the  larger  the  area  the  greater  the 
number  of  nerve  fibres  stimulated.^  If  the  stimulus  were 
the  physical  pressure  exerted,  the  intensity  would,  we  think, 
Increase  with  the  area.  For  not  only  are  more  nerves  acted 
on  by  larger  areas,  but  the  pressure  increases  in  direct  pro- 
portion to  the  area,  provided  the  force  applied  be  constant. 
As  the  exact  reverse  effect  is  produced  upon  the  sensory 
end  organs,  the  stimulus  can  not  be  considered  mere  pres- 
sure, but  rather  as  work  done  upon  the  skin  and  subcutane- 
ous tissues. 

In  sensations  of  impact  the  stimulus  is,  as  we  have  seen, 
the  energy  of  the  moving  mass  or  a  quantity  more  approach- 
ing to  the  momentum.^  In  the  case  of  impact  stimuli,  there- 
fore, we  should  not  expect  the  intensity  of  the  sensation  to  in- 
crease, but  rather  to  diminish  with  the  area.  For  the  greater 
the  area  the  less  the  energy  or  momentum  transferred  to  the 
dermal  tissues  within  a  given  area.  When  no  impact,  but 
only  pressure,  is  exerted,  then  the  stimulus  is  the  work 
expended  in  overcoming  the  resistance  of  the  skin.  The 
work  done  is  independent  of  the  area  of  stimulation,  as  it  de- 
pends upon  the  impressed  forces.  Consequently,  the  greater 
the  area  the  less  is  the  work  done  at  any  one  point  in  the 
region  affected  by  the  pressure ;  in  other  words,  the  less 
the  intensity  of  stimulation.  If,  moreover,  the  function  of 
the  touch  corpuscles  be  protective,  as  some  suppose,  the 
stimulus  will  meet  with  greater  resistance,  the  greater  the 
area  upon  which  it  acts. 

^  Weber,  op.  cit.,  553;  also  Dessoir,  op.  cit.,  297. 
' Miiller-Lyer,  Archiv  fur  Anat.  und  Physiol.,  1889,  Supp.  Bd. 
'  Funke  even  states  that  the  intensity  increases  with  the  area.      Op.  cit.,  331. 
*The  movement  theory  of  haptic  stimulation  was,  we  believe,  first  advanced  by 
Lotze,  Med.  Psychologic,  198. 


THE  AREA   OF  STIMULATION. 


73 


This  leads  us  to  the  consideration  of  the  peculiar  phe- 
nomena of  dermal  pressure  from  liquid  or  gaseous  bodies. 
The  atmosphere  exerts  a  pressure  upon  the  body  of  1.03 
k.  per  sq.  centimeter,  but  has  no  effect  upon  conscious- 
ness. When  the  hand  is  placed  in  a  fluid,  even  of  consider- 
able density,  no  pressure  is  felt  except  at  the  surface.  These 
phenomena  are  intelligible,  when  we  consider  that  the  pro- 
cess of  haptic  stimulation  involves  a  transference  of  energy. 
The  element  of  time  is  of  not  a  little  importance,  but  will  be 
considered  later.  The  ring  effect  observed  when  the  hand 
is  plunged  in  mercury  has  its  counterpart  in  the  relatively 
great  intensity  of  pressure  sensations  from  solid  stimuli  in 
the  region  of  the  perimeter  of  the  surface  applied.  A  kilo- 
gram weight  placed  on  the  hand  will  be  felt  most  distinctly 
at  the  edge.  That  the  skin  is  more  affected  in  this  region  is 
shown  by  the  dark  red  line  from  vaso-motor  disturbance 
that  here  appears  when  the  stimulus  is  removed.  It  is  not 
necessary,  therefore,  to  explain  the  phenomena  by  such 
hypotheses  as  that  of  Meissner,  who  held  that  the  process  of 
pressure  stimulation  was  an  oscillatory  action  in  the  tactile 
corpuscles.^ 

Sec.  5-    Tlie  Area    of  Stimulation   and   the  Discriininatio7i   of 
Intensity. 

In  the  chapter  on  the  accuracy  of  discrimination  for 
different  intensities,  two  areas  were  used,  8  cm.  and  -^-^  cm., 
approximately.  In  addition  to  the  experiments  there  de- 
scribed, 1000  experiments  were  made  on  W.  In  500  of 
these  the  larger  area  was  used,  and  in  the  other  500  the 
smaller  area.  In  the  following  table  will  be  found  the  prob- 
able and  constant  errors  based  upon  each  set  of  100  experi- 
ments. 

Stimulus,  200  g. 


Area. 

Pi 

P2 

P3 

p, 

Ps 

Av.  P. 

Ci 

C2 

C3 

C4 

Cs 

Av.C. 

8  cm. 

37 

19. 

22. 

20. 

14- 

22. 

15 

10 

15 

9 

5 

II 

^cm. 

33 

56 

10. 

14 

16 

25 

32 

8 

9 

3 

12 

13 

1  Meissner,   Zeit.  filr  Rat.   Med.,   3'^  R.,  VII.      Cf.   Funke,   op.  cit.,  328,  for  a 
criticism  of  Meissner's  theory. 


74 


SENSATIONS  FROM  PRESSURE  AND  IMPACT. 


From  these  results  it  is  evident  that  the  accuracy  of  dis- 
crimination of  this  observer  was  not  on  the  whole  appre- 
ciably altered  by  the  variation  of  the  area.  The  same  might 
be  said  of  the  constant  error.  The  variation  of  the  probable 
error  for  the  smaller  area  is,  however,  so  great  that  in  spite  of 
the  large  number  of  experiments,  the  results  do  not  admit  of 
an  exact  interpretation.  By  comparing  the  average  values  of 
p 

—  for  the  observers  S.  F.,  J.  S.  and  L.  S.,  on  whom  experi- 
ments were  made  for  both  areas,  we  obtain  somewhat  more 
satisfactory  results.  By  referring  to  the  tables,  Chap.  Ill, 
Sec.  3,  we  see  that  although  N.  F.'s  probable  errors  are 
very  variable,  especially  for  the  smaller  area,  those  of  L.  S. 
for    both    areas   are    fairly    constant.      The    following    table 

p 

^ives  the  average  values  of  — '  the  probable  error  divided  by 

the  stimulus,  for  all  intensities  used. 


Area. 

p 

Average  values  of    — • 
o 

N.F. 

J.  S. 

L.  S. 

W. 

8  cm. 
■i^  cm. 

•13 
.18 

.  1 1 

.  12 

.10 
.  lO 

.  1 1 
.13 

Although  W.  and  N.  F.  appear  to  judge  stimuli  of  the 
larger  area  more  accurately,  there  is  no  appreciable  difference 
lor  J.  S.  and  L.  S.,  the  most  constant  of  the  four  observers. 

Sec.  6.    The  hitensity  of   Stimulatio7i  and  the  Discrimination 
of  Areas. 

It  was  not  our  purpose  to  enter  into  a  discussion  of  the 
problem  of  tactile  space  perception.  But  having  found  that 
the  discrimination  of  intensity  was  not  uniformly  affected 
by  the  area  of  stimulation,  the  question  suggested  itself 
whether  the  converse  was  true.  For  the  purpose  of  finding 
if  this  were  so,  weights  were  used  of  200  g.  and  800  g.     Two 


THE  AREA   OF  STIMULATION. 


75 


standard  areas  were  used,  being  approximately  32  mm.  and 
1 1.3  mm.  in  diameter,  and  therefore  800  mm.  and  100  mm. 
in  area.  The  bases  of  the  boxes  applied  were  covered  with 
stiff  paper  cut  so  as  to  be  circular  in  shape.  We  were  not 
investigating  the  absolute  accuracy  of  discrimination  of 
areas,  nor  yet  the  relation  of  this  to  the  magnitude  of  the 
area;  consequently  any  errors  due  to  the  method  of  obtain- 
ing the  different  areas  may  be  neglected.  The  probable  and 
constant  errors  given  in  the  tables  are,  of  course,  in  millime- 
ters. They  were  obtained,  as  in  other  experiments,  by  the 
method  of  right  and  wrong  cases,  from  the  percentage  of 
right  answers  in  a  hundred  experiments.  In  these  experi- 
ments the  area  is  considered  the  stimulus,  S,  and  the  incre- 
ment A,  is  the  difference  between  the  area  of  the  standard, 
100  or  800  mm.,  and  that  of  the  area  to  be  compared.  The 
magnitude  of  the  increment  is  obtained  by  the  equation, 

A  =  TT  (r^  —  r,2,)  =  TT  (r  4-  r^,)  (r  —  r^,), 

in  which  r  and  rj  are  the  radii  of  the  bases.  The  first  of  the 
two  tables  gives  the  results  for  three  observers,  the  smaller 
area  being  used.  The  second  table  gives  corresponding 
results  for  the  larger  area.  But  100  experiments  were  made 
upon  N.  F.  and  W.  for  each  of  the  probable  errors  calcu- 
lated. The  probable  errors  for  L.  S.,  however,  are  each 
calculated  from  the  results  of  300  experiments. 


Area,  100  mm. 


Probable  Error. 

1 

Weight. 

L.  S. 

N.  F. 

W. 

Av. 

200  g. 
800  g. 

43 
31^ 

40 

21 
47 

31 
39 

Ar 

ea,  800  mm. 

200  g. 
800  g. 

73 
91^ 

47 
70 

41 
69 

53 
71 

*  A  weight  of  looo  g.,  instead  of  800  g. ,  was  used  in  experiments  on  L.  S. 


^6  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

The  figures  above  given  show  that  the  discrimination  for 
areas  is  not  as  accurate  for  the  high  intensity,  the  probable 
errors  for  800  g.  being  in  four  cases  out  of  five  much  greater 
than  for  200  g.  The  one  exception  appears  in  the  experi- 
ments on  L.  S.  for  the  smaller  area.  In  conducting  these 
experiments,  however,  it  was  found  that  the  accuracy  of 
discrimination  for  800  g.  increased  to  such  an  extent  from 
practice  that  the  variable  area  had  to  be  changed  in  order 
that  the  increment  might  not  be  too  great  for  accurate  cal- 
culation of  the  probable  error.  In  the  first  few  experiments 
made,  then,  the  accuracy  of  discrimination  was  undoubtedly 
much  less  for  800  g.  than  for  200  g.  There  was,  however^ 
no  appreciable  improvement  from  practice  after  thirty  or 
forty  experiments.  The  apparent  exception,  therefore,  par- 
tially confirms  the  results  obtained  for  the  other  observers. 

If  we  compare  the  second  table  with  the  first,  we  note 
that  the  probable  error  for  the  larger  area,  although  appre- 
ciably greater,  does  not  increase  in  proportion  to  the 
areas.  It  is  possible  that  in  these  experiments  what  is  really 
discriminated  is  the  linear  relation,  that  is,  the  relative 
diameters  of  the  circles.  This  is,  however,  not  probable ; 
for  the  difference  felt  seems  to  be  a  qualitative  difference  in 
the  sensations  from  which  that  of  space  is  inferred.  The 
change  in  sensation  corresponding  to  change  in  the  area  of 
stimulation  might,  indeed,  be  supposed  to  be  merely  a  quan- 
titative change  in  extensity.  But  the  great  difficulty  observ- 
ers have  of  comparing  intensities  of  different  areas  confirms- 
the  results  of  the  writer's  introspection,  that  this  change  in. 
sensation  is  not  primarily  a  spatial  change. 


CHAPTER  VII. 

The  Time  of  Stimulation. 

Sec.  I.    The  Intensity  of  Haptic  Sensations  in  Relation  to  the 
Tifne  :     Low  Intensities. 

The  intensity  of  visual  and  temperature  sensations  is 
clearly  related  to  the  time  of  stimulation.  But  if  a  weight 
of  low  intensity,  and  of  not  too  small  an  area,  be  applied  to 
the  skin,  the  resulting-  sensation  will  continue  but  a  few  sec- 
onds, and  will  not  increase,  as  might  be  expected,  with  the 
time  of  application.  It  is  largely  on  this  principle  that  the 
phenomena  of  gaseous  and  liquid  pressure  may  be  explained. 
The  pressure  of  the  atmosphere  is  fairly  constant,  and  is, 
therefore,  not  perceived.  Meissner  observed  that  melted 
wax  allowed  to  harden  on  the  hand  had  no  sensory  effect, 
although  his  explanation  is  different  from  that  here  given. 
When  the  hand  is  plunged  in  mercury  and  held  in  the  same 
position,  the  pressure  remains  constant,  and  it  is  only  when 
the  hand  is  moved  that  the  pressure  sensation  is  distinct.^ 
Hall  and  Motora  found,  contrary  to  what  we  might  expect, 
that  the  discrimination  of  gradual  pressure  change  was  best 
for  the  slowest  rate  of  change  of  stimulus  that  was  used, 
^^  of  the  stimulus  per  second.^  In  these  experiments  the 
observer  had  first  to  decide  whether  the  stimulus  was  increas- 
ing or  decreasing ;  and  it  is  probable  that,  as  suggested  by 
the  writers,  the  cause  of  the  decrease  in  the  accuracy  of  dis- 
crimination was  the  distracting  effect  of  sudden  changes 
upon  the  attention,  and  consequently  upon  the  accuracy  of 
perception. 

We  intended  to  make  experiments  on  judgments  of  in- 
tensity in  relation  to  the  time  of  stimulation,  but  the  appa- 

^  Cf.  Meissner,  op.  cit. 

^  Hall  and  Motora,  Am.  Journ.  Psy.,  I,  87. 

77 


yS  SENSA  TIONS  FROM  PRESSURE  AND  IMPACT. 

rent  impossibility  of  eliminating  the  error  arising  from 
memory  of  the  standard  stimulus  led  us  to  confine  ourselves 
to  qualitative  observations.  We  did,  however,  make  experi- 
ments on  the  intensive  effect  of  the  time  for  stimuli  of  such 
low  intensity  as  to  be  perceived  with  difficulty.  The  instru- 
ment used  was  that  already  described,  by  which  pressure 
was  exerted  by  the  hand  of  the  experimenter.^  There  was 
no  means  of  regulating  the  rate  of  application  of  the  pres- 
sure except  the  judgment  of  the  experimenter,  and  the 
results  must  therefore  be  considered  as  inexact.  The  ex- 
perimenter practised  himself  in  increasing  the  pressure  at 
such  a  rate  that  it  took  8-10  sec.  to  reach  a  pressure  of  .4  g. 
In  like  manner  a  time  of  1-2  sec.  was  obtained.  The  third 
time  of  application  was  the  shortest,  i— ^-  sec,  the  increase 
being  as  rapid  as  was  consistent  Avith  accuracy.  The  rates 
of  increase  were,  therefore,  .05-.04g.,  .\-.2  g.  and  2.3-1.6  g. 
per  sec.  The  maximum  pressure,  .4g.,  was,  of  course,  kept 
fairly  constant.  Fifty  experiments  were  made  for  each  rate 
by  the  writer  on  S.  F.,  and  as  man}^  by  S.  F.  on  the  writer. 
In  the  tables  below  are  the  percentages  of  times  the  stimu- 
lus .4  g.  was  perceived  at  the  different  rates  of  increase. 

•05--04  g-  •4--2  g.  2.3-1.6  g. 

per  sec.  per  sec.  per  sec. 

S.  F.       -        -          10%                  34f.  82 f. 

G.            .        .           2%                 30%  82^ 

Av.          -        -           6%                 32%  82% 

From  these  results  it  is  evident  that  the  sensory  effect  of 
pressure  stimuli  increases  with  the  rate  of  application.  This 
is  what  we  should  expect  on  the  assumption  that  the  inten- 
sity of  pressure  sensations  decreases  rapidly  with  the  time 
of  application. 

As  for  the  theoretic  interpretation  of  these  results,  we 
judge  them  corroborative  of  the  movement  theory  of  dermal 
stimulation.  The  stimulus  is  not  to  be  considered  mere 
pressure,  but  the  energy  expended  upon  the  dermal  tissues. 
From  this  point  of  view  we  are  not  justified  in  identifying 
the  time  of  application  of  a  pressure  stimulus  with  the  time 

^  See  Chap.  II,  Sec.  ■?. 


THE   TIME  OF  STIMULATION.  79 

of  actual  stimulation.  If  a  vibrating  tuning-fork  of  suffi- 
cient amplitude  to  cause  a  distinct  sensation  be  placed  in 
contact  with  the  skin,  there  is  continued  intermittent  stimu- 
lation, and  the  sensation  does  not  decrease  as  when  a  pres- 
sure stimulus  is  applied.  The  intermittent  process  of  stimu- 
lation by  the  tuning-fork  is  similar  to  that  of  visual  and 
auditory  stimulation,  for  the  physical  stimuli  are  successive 
transformations  of  energy. 

The  time  phenomena  of  pressure  stimulation  may  also  be 
brought  under  the  general  law  that  it  is  not  static  condi- 
tions, but  changes  in  the  environment  that  give  rise  to  the 
'nervous  shock'  of  Spencerian  psychology.  It  is  such 
conditions  of  the  environment  that  the  organism  needs  to 
perceive  in  order  to  coordinate  its  motor  activities  for  pur- 
poses of  self-preservation  and  reproduction.  The  cataplec- 
tic  shock  so  frequently  experienced  when  one  is  unexpect- 
edly addressed,  shows  how  sensitive  the  central  nervous 
system  is  to  sudden  peripheral  changes.  But  we  need  not 
depend  only  upon  observation  for  proofs  of  this  principle. 
It  is  well  known  that  motion  on  the  skin  may  be  perceived 
within  the  circumference  of  Weber's  sensor  circles;  and 
Hall  and  Donaldson  found  that  the  perception  of  motion  is 
independent  of  direction,  and  is  clearest  immediately  after 
the  motion  begins.^  In  fact,  the  time  phenomena  of  dermal 
sensations  point  clearly  to  the  difference  theory  of  sensation, 
'according  to  which  change  in  the  objective  environment  and 
in  the  subjective  mind  is  the  sine  qua  non  of  sensation.^  The 
psychological  generalization  has,  moreover,  a  demonstrable 
physiological  basis.  Only  on  making  or  breaking  an  elec- 
tric circuit  is  a  motor  nerve  stimulated.  More  closely  bear- 
ing on  our  problem  are  the  experiments  of  Fontana,  who 
found  that  pressure  could  be  applied  so  gradually  as  to  kill  a 
motor  nerve  without  inducing  muscular  contraction.  Simi- 
lar results  have  been  obtained  for  temperature  stimuli.^ 


^Hall  and  Donaldson,  Mind,  X,  556. 

*Cf.  Hoffding,  op.  cit.,  138,  141  ;  Dessoir,  op.  cit.,  188 

^  Heinzmann,  Archiv.  fiir  gesammte  Physiol.,  VI,  222. 


8o  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

Sec.  2.   High  Intensities. 

When  stimuli  beyond  a  certain  intensity  are  applied,  the 
phenomena  are  quite  different.  If  a  kilogram  weight  be 
placed  on  the  hand,  the  intensity  of  the  sensation  seems 
gradually  to  increase  and  to  pass  into  pain.  Miiller  observed 
that  a  sensation  of  pricking  and  of  having  a  limb  '  asleep  ' 
could  be  caused  by  long-continued  pressure  stimulation.^ 
Similar  observations  on  temperature  stimuli  were  made  by 
Weber.  Thus  it  appears  that  heterogeneous  sensations 
may  be  caused  by  variations  in  the  time  of  application  of 
dermal  stimuli. 

For  the  purpose  of  investigating  the  relation  between  the 
time  of  pressure  causing  pain  and  the  intensive  pain  thres- 
hold, weights  of  different  magnitudes  were  placed  in  a  bal- 
ance pan  so  as  to  act  on  a  constant  area  of  the  palm  of  the 
hand,  and  the  time  was  noted  which  elapsed  before  the  ap- 
pearance of  pain.  To  the  under  side  of  the  balance  pan  a 
wooden  piece  was  fastened,  the  circular  end  of  which,  1.5  mm. 
in  diameter,  came  in  contact  with  the  palm  of  the  hand. 
The  longer  times  were  recorded  by  a  watch,  and  the  shorter 
times  by  the  Hipp  chronoscope,  a  Morse  key  being  so  placed 
that  the  observer  could  close  the  circuit  as  he  applied  the 
weight  without  appreciable  error.  The  place  of  stimulation 
was  varied  within  a  radius  of  about  i  cm.  ;  otherwise  there 
would  have  been  danger  of  alterations  in  the  condition  of  the 
skin  at  the  place  of  stimulation  as  the  experiments  pro- 
gressed. Ten  experiments  were  made  for  each  weight  on 
two  observers,  S.  F.  and  the  writer.^  But  one  experiment 
for  a  given  weight  was  made  on  any  one  day,  and  not  more 
than  three  or  four  times  a  week  were  these  experiments 
made.  The  order  of  half  of  the  experiments  was  the  reverse 
of  that  of  the  other  half.  The  figures  below  indicate  the 
time  in  seconds  for  the  various  stimuli  to  cause  pain.  Only 
the  averages  are  given,  together  with  their  probable  errors. 


^  Quoted  by  Weber,  op.  cit. 

^  Experiments  were  begun  on  another  observer,  but  were  not  completed.  It  was 
evident,  however,  that  results  would  have  been  obtained  similar  to  those  obtained  for 
G.  and  S.  F. 


THE   TIME  OF  STIMULA  TION. 


81 


Observer. 

100  g. 

200  g. 

300  g. 

500  g. 

S.  F.   .  . 
G.  .  .  . 

294  =t  30. 

167  rb  17. 

37  ±  3-6 
34±  2.7 

8.  ±  .9 
12  =b  1.5 

3-3  ±  .2 
6.  ±  .06 

The  results  shown  above  are  represented  graphically  in 
the  accompanying  curves. 

Figure  9. 
Time 


iioo 


^°°    Intensity 


The  experiments  prove  beyond  question  that  the  pain 
threshold  is  functionally  related  to  the  time  as  well  as  the 
intensity  of  stimulation.  The  results  obtained  are  not 
sufficiently  exact  to  admit  of  an  analytical  expression.  It 
appears  that  the  time  curve  approaches  O  as  its  limit  for 
high  intensities,  and  that  for  low  intensities  it  either  increases 
indefinitely  or  approaches  as  its  limit  an  asympotic  line 
parallel  to  the  axis  T.  That  the  ascending  branch  does 
approach  a  limit  is  evident  from  introspective  observation. 
Weights  of  low  intensities  soon  cease  to  be  perceptible,  and 
never  become  painful.  Thus  the  clothing  we  wear  exerts 
continual  pressure,  but  is  never  painful.  The  curves  ob- 
tained may  be  said,  therefore,  to  resemble  rectangular  hyper- 
bolas. If  the  relation  between  the  time  and  intensity  caus- 
ing pain  could  be  thus  represented,  it  would  be  expressed 
analytically  by  the  equation, 

(I-h)T:^k, 


82  SEA^SATIONS  FROM  PRESSURE  AND  IMPACT. 

in  which  h  is  a  constant,  being  the  intensity  below  which 
stimuli  are  never  painful.  To  obtain  the  relation  between 
the  time  and  intensity  having  equal  intensive  effects  as  the 
sensation  increases  in  intensity,  we  can  substitute  in  the 
above  equation  the  reciprocal  of  T,  since  the  intensive  effect 
would  of  course  decrease  as  the  threshold  increases.  We 
then  have, 

k        k' 

From  this  equation,  that  of  a  straight  line,  we  see  that  as 
regards  their  intensive  effect  on  pain  sensations,  the  inten- 
sity and  time  of  the  stimulus  increase  in  direct  proportion. 

A  striking  feature  of  the  above  experiments  is  the  great 
variation  in  the  time  before  the  pain  appears.  This  is, 
however,  only  partially  a  true  variation.  It  is  generally 
difficult  to  decide,  especially  for  low  intensities,  when  the 
stimulus  becomes  painful.  This  is  quite  the  contrary  of 
what  we  found  to  be  the  case  when  the  intensive  threshold 
was  being  determined.  There  is,  however,  no  constancy 
even  in  the  manner  of  variation.  At  times  for  the  lOO  g. 
stimulus  the  pain  would  come  very  suddenly,  only  to  cease 
and  reappear,  but  generally  the  appearance  of  pain  was  very 
gradual.  The  sensation  seemed  to  increase  in  intensity 
before  the  pain  was  distinctly  felt.  In  the  experiments  on 
100  g.  a  latent  period  seemed  to  elapse  before  any  appre- 
ciable increase  in  intensity  began.  This  latent  period  for 
S.  F.  seemed  to  be  on  the  average  about  half  of  the  total 
time.  The  two  observers  disagreed  as  to  whether  there  was 
any  appreciable  decrease  in  intensity  before  the  increase 
began. 

We  are  not  justified  in  assuming  that  the  relation  be- 
tween the  time  of  pressure  and  the  intensity  of  pain  holds 
also  for  pressure  sensations.  The  gradual  appearance  of 
the  dermal  pain,  preceded  by  an  apparent  increase  of  pres- 
sure intensity,  undoubtedly  points  to  such  a  conclusion. 
But  the  results  admit  of  another  interpretation.  It  is  quite 
possible  that  the  mind  confuses  the  incipient  pain  with  the 
pressure  sensation.  As  we  know  dermal  pain  to  be  related 
to  the   intensity  of  the  stimulus,  and  as  we  are  not  accus- 


THE   TIME  OF  STIMULATION.  83 

tomed  to  think  so  much  of  the  time  as  a  factor,  it  is  but 
natural  that  we  should  judge  the  change  in  sensation  to  be 
due  to  more  intense  stimulation.  We  should  then  consider 
this  change  an  intensive  change,  until  the  painful  element 
became  so  clear  as  to  be  distinct  in  consciousness.  That  it 
is  difficult  to  distinguish  heterogeneous  sensations  of  very 
low  intensity  is  shown  by  the  experiments  of  Wunderli.^ 

Moreover,  our  experiments  are,  we  think,  corroborative 
of  the  theory  that  sensations  of  pain  and  pressure  are  utterly 
disparate.  For,  otherwise,  how  could  we  explain  the  fact 
that  the  intensity  of  pain  increases  with  the  time,  whereas 
the  intensity  of  pressure  sensations,  at  least  for  low  intensi- 
ties, decreases  rapidly  with  the  time  ?  Equally  difficult  to 
account  for  on  the  algedonic  tone  theory  is  the  continuation 
of  the  pain  after  the  cessation  of  stimulation,  which  was 
very  marked  for  100  g. 

But  if  pain  be  a  distinct  sensation,  with  a  distinct  physi- 
cal basis,  the  results  are  quite  intelligible.  From  this  point 
of  view,  we  can  understand  how  pressure  without  appre- 
ciable transformation  of  energy  can  be  considered  a  stimu- 
lus to  pain.  Unlike  haptic  sensations  proper,  dermal  pain 
furnishes  the  sensory  data  for  perceptions,  not  of  the  object- 
ive environment,  but  of  the  subjective  self;  and  may,  there- 
fore, be  induced  by  any  stimulus  of  sufficient  intensity. 
This  view  finds  further  support  in  teleological  considera- 
tions. If  pain  exist  for  the  purpose  of  warning  the  higher 
centres  of  injury  done  to  the  tissues,  the  intensity  of  pain 
would,  we  should  expect,  be  related  to  the  time  of  pres- 
sure ;  for  the  longer  the  time  of  pressure  the  greater  the 
resultant  injury  to  the  tissues. 

^  See  Ch.  I,  Sec.  2. 


SUMMARY. 

We  shall  now  present  a  brief  summary  of  the  more  im- 
portant results  of  the  investigations  described  in  the  preced- 
ing pages. 

A. — Experimental. 

1.  Hot  and  cold  stimuli  are  overestimated  for  low  inten- 

sities, but  not  for  high  intensities. 

2.  The  estimate   of  the  intensity  of   haptic   stimuli  in- 

creases for  low  intensities  much  more  slowly 
than  the  stimulus  ;  but  as  the  stimulus  approaches 
the  pain  threshold,  the  estimate  of  intensity  in- 
creases much  faster. 

3.  The  intensive  pain  threshold,  for  pressure  acting  on 

.5  cm.  of  the  hand,  varies  greatly  with  individ- 
uals, the  average  being  5400  g.  Age  and  sex 
appear  to  have  less  effect  than  individual  differ- 
ences. 

4.  The  average  value  of  the  least  perceptible  pressure 

acting  on  an  area  of  .9  cm.,  the  rate  of  increase 
being  about  .3  g.  per  sec,  was  1.9  g.  for  S.  F. 
and  2.6  g.  for  G.  The  intensive  range  of  haptic 
sensations  for  these  observers,  as  based  upon 
these  measurements,  was  about  1700. 

5.  Weber's  law  holds  approximately  for  weights  greater 

than  100  to  500  g.  For  low  intensities  the  prob- 
able error  increases  much  more  slowly  than  the 
stimulus. 

6.  The  average  value  of  the  ratio  of  the  probable  error 

to  the  stimulus  for  stimuli  of  from  100  g.  to  3000 
g.  is  ^. 
84 


SUMMARY.  85 

7.  The  constant  error  is  frequently  very  great  for  pres- 

sure stimuli.  It  increases  with  the  stimulus,  but 
the  relation  is  complex,  and  is  subject  to  great 
individual  variations.  Some  observers  have  no 
constant  error  except  for  stimuli  of  very  great 
intensity.  The  constant  error  is  more  variable 
than  the  probable  error.  Its  magnitude  seems 
inversely  related  to  the  accuracy  of  discrimina- 
tion. A  great  constant  error  for  pressure  does 
not  necessitate  one  for  lifted  weights. 

8.  The  degree  of  confidence  in  the  perception  of  inten- 

sive differences  varies  greatly  for  individuals,  the 
proportion  of  wrong  judgments  of  which  observ- 
ers were  confident  ranging  from  \  to  5^^.  The 
probability  of  correctness  when  confident  was 
for  most  observers  from  .8  to  .9.  There  is  no 
relation  between  either  of  these  quantities  and 
the  accuracy  of  discrimination.  The  percentage 
of  correct  guesses  varied  from  52%  to  70%,  the 
average  being  59/^. 

9.  The  accuracy  of  discrimination  for  weights  of   100  g. 

or  more  is,  on  the  average,  not  appreciably  differ- 
ent for  the  palm  of  the  hand,  the  back  of  the 
hand  and  the  volar  surface  of  the  index  finger. 
For  5-7  g.  the  accuracy  of  discrimination,  as 
found  from  one  observer,  for  the  palm  of  the 
hand  and  the  back  of  the  forearm,  is  less  than  for 
the  index  finger,  but  improves  greatly  by  prac- 
tice. 

10,  Stimuli  of  low  intensity  placed  on  the  forearm,  are 

judged  lighter  than  when  placed  on  the  palm  of 
the  hand  or  the  index  finger. 

1 1.  The  pain  threshold  for  pressure  varies  with  the  place 

of  stimulation,  being  greatest  where  the  skin  is 
thick  and  separated  from  the  bone  by  muscular 
tissues.  The  temporal  region  of  the  head  is  the 
most  sensitive,  and  the  palm  of  the  hand,  the 
thigh,  and  the  heel,  are  among  the  least  sensitive 
parts. 


86  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

12.  Weights  of  .01  g.  are  about  as  easily  perceived  when 

impact  is  not  entirely  excluded,  as  weights  of  ,4  g. 
when  pressure  only  is  applied,  the  time  of  appli- 
cation being  1-2  sec. 

13.  The  pain  threshold  for  impact  stimuli  is  determined 

by  the  product  of  the  mass  and  the  square  of  the 
velocity. 

14.  In  judgments  of  the  intensity  of  impact  stimuli  the 

mass  has  in  general  more  effect  than  the  square  of 
the  velocity,  but  less  than  the  velocity. 

15.  Differences  in  velocity  are   perceived,  on  the  whole, 

more  accurately  than  differences  in  mass,  but 
much  less  accurately  than  differences  in  the 
square  of  velocity.  Individuals  differ  greatly, 
however. 

16.  The  discrimination  for  moving  weights  is  about  the 

same  as  for  weights  applied  without  appreciable 
impact. 

17.  The  area  of  stimulation  does  not,  on  the  whole,  affect 

the  accurac}^  of  discrimination  for  weights.  But 
individual  peculiarities  appear  in  the  results 
obtained. 

18.  Pressure  stimuli  of  small  area  are  generally  overes- 

timated. The  extent  of  overestimation  of  inten- 
sity for  an  area  -g-^^  of  8  cm.  was  on  the  average  \. 

19.  The  probability  that  a  stimulus  of  very  low  intensity 

will  be  perceived  is  inversely  related  to  the  area 
of  stimulation. 

20.  The  pain  threshold  increases  with  the  area  of  stimu- 

lation in  approximately  a  logarithmic  proportion, 

21.  The  discrimination  of  areas  is  much  better  for  stimuli 

of  200  g.  than  for  stimuli  of  800  g. 

22.  The  relative  accuracy  of  discrimination  for  areas  is 

not  constant,  but  is  greater  for  large  areas. 

23.  The  probability  that   pressure  stimuli  of   very  low 

intensity  will  be  perceived  increases  with  the  rate 
of  increase  of  the  stimulus. 

24.  The  relation  between  the  time  and  intensity  threshold 

of  pain  is  approximately  expressed  by  an  hyper- 


SUMMAR  Y.  87 

bolic  curve.  The  appearance  of  pain  as  the  time 
of  stimulation  is  increased,  is  generally  very 
gradual  and  difficult  to  determine.  There  is  an 
intensive  limit  below  which  stimuli  never  cause 
pain. 

B. — Theoretical. 

1.  There  is  no  basis  for  the  alleged  identity  of  haptic 

and  temperature  sensations. 

2.  Pain,  tickle  and  pressure  sensations  are  heterogeneous 

sensations  induced  by  quantitative  changes  in  the 
intensity  of  the  stimulus.  Dermal  pain  itself  is 
probably  a  sensation  and  not  merely  an  intensive 
form  of  the  algedonic  tone. 

3.  Touch  and  pressure  sensations  are  qualitatively  the 

same.  The  apparent  difference  between  them  is 
really  one  of  perceptive  processes. 

4.  The  so-called  threshold  is  not  a  true  quantity.     This 

may  be  shown  by  the  same  arguments  that  are 
applied  to  the  so-called  least  noticeable  difference. 

5.  If  the  estimate  of  the  intensity  of  the  stimulus  may  be 

considered  as  indicative  of  a  corresponding  in- 
crease in  the  intensity  of  sensation,  this  quantity 
increases  much  more  slowly  than  the  stimulus. 
The  apparent  rapid  increase  for  very  high  inten- 
sities may  be  due  to  perceptive  processes  and  not 
be  a  true  increase  in  sensation. 

6.  The  variation   of  the  probable   and  constant  errors 

renders  inexact  the  use  of  the  probability  integral 
in  the  method  of  right  and  wrong  cases. 

7.  The  variations  in  the  confidence  of  observers  and  in 

the  percentage  of  right  cases  in  guessing,  goes  to 
prove  that  there  is  no  such  quantity  as  a  least 
noticeable  difference. 

8.  The  accuracy  of  discrimination  is  in  general  probably 

independent  of  the  place  of  stimulation,  except 
for  very  low  intensities,  which  have  less  intensive 
effect  at  some  places  than  at  others.  Practice 
seems  to  aid  the  discrimination  at  places  not 
accustomed  to  pressure  stimuli. 


88  SENSATIONS  FROM  PRESSURE  AND  IMPACT. 

9.  The  intensive  effect  of  impact  stimuli  for  pain  is 
equally  dependent  upon  the  mass  and  the  square 
of  the  velocity.  The  intensive  efiect  for  such 
stimuli  causing  only  impact  sensations  apparently 
increases  faster  for  the  velocity  than  the  mass, 
but  more  slowly  for  the  square  of  velocity  than 
for  the  mass.  If  this  be  true,  the  stimulus  for 
impact  sensations  is  different  from  that  for  pain 
sensations,  the  stimulus  for  pain  being  mv^  and 
that  for  impact  sensations  being  mv^,  in  which  k 
is  somewhat  greater  than  unity,  and  possibly  sub- 
ject to  individual  variations. 

10.  The  intensity  of  dermal  sensations,  is  inversely  re- 

lated to  the  area  of  stimulation.  If  we  assume 
any  of  the  psycho-physical  laws  deduced,  the 
intensity  of  the  sensation  increases  much  more 
slowly  than  the  reciprocal  of  the  logarithm  of 
the  area. 

11.  The  intensive  effect  of  the  area  may  be  explained  by 

the  probable  physiological  process  of  stimulation, 
the  effect  upon  the  sensory  nerves  being  dependent 
upon  the  energy  expended  upon  the  surrounding 
tissues.  The  stimulus  in  pressure  sensations  is 
not  to  be  considered  the  force  applied,  but  the 
work  done  by  this  force,  or  more  strictly  the 
energy  lost  by  the  mass  applied. 

12.  The  intensity  of  pressure  sensations  decreases  for  low 

intensities  with  the  time  of  pressure.  For  high 
intensities  causing  pain,  the  intensity  of  the  sen- 
sation of  pain  increases  with  the  time  of  pressure. 
The  relation  of  the  intensive  effects  of  the  time 
and  that  of  the  intensity  of  stimulation  for  pain 
sensations  is  probably  that  of  a  direct  proportion. 

13.  The  time  phenomena  of  dermal  stimulation  support 

the  theory  advanced  as  to  the  process  of  stimula- 
tion. They  also  tend  to  show  that  dermal  pain 
is  a  distinct  sensation. 


VITA. 

I  was  born  in  St.  Louis,  Missouri,  July  4th,  1869.  I 
entered  the  University  of  New  York  in  1886,  having  been 
prepared  for  college  principally  by  private  study.  In  1887 
I  entered  the  Sophomore  Class  of  the  School  of  Arts,  Col- 
umbia College,  and  graduated  in  1890.  Since  that  time  I 
have  pursued  post-graduate  studies  under  the  University 
Faculties  of  Philosophy  and  Pure  Science ;  in  Psychology, 
with  Prof.  Cattell;  in  the  History  of  Philosophy,  with 
Prof.  Butler,  Dr.  Hyslop,  and  Prof.  Peck  (Roman  Philoso- 
phy); in  Biology,  with  Prof.  Osborn,  Prof.  Wilson,  and  Dr. 
Lee;   in  Physics,  with  Prof.  Rood  and  Prof.  Pupin. 

HONORS   AND    DEGREES    CONFERRED    UPON     THE    WRITER. 


Scholarship  in  Latin,  il 
''  "   Greek,  i\ 

)  "■  "  Greek,  1889. 

Degree  of  Bachelor  of  Arts,  with  Honors  in  Philosophy, 
Classics  and  English,  1890. 

Prize  Fellowship  in  Letters,  1890-91. 
University  Fellowship  in  Philosophy,  1891-93. 

PREVIOUS    PUBLICATION. 

J.  H.  Lambert:  "  A  Study  in  the  Development  of  the 
Critical  Philosophy,"  Tke  Philosophical  Review,  January, 
1893. 


89 


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